how to solve the 12 equations in an effective way

i have tried but is there an effective way to solve the 12 equations with 12 variables?

function program are as this

function F = root2d(x)
%syms equa1sub equa2sub equa3sub equa4sub equa5sub equa6sub;
equa1sub =x(1)[phone]/281474976710656-(4154756651791824122955846205623/10141204801825835211973625643008+10968068365840776354319913193387/10141204801825835211973625643008*i)*x(7)+15954949269969134648023144147861/83076749736557242056487941267521536*x(8)-71813660819499486824121496911249/680564733841876926926749214863536422912*x(9)+68704458373558018815486967994675/1393796574908163946345982392040522594123776*x(10)-26218118780833903306440628355937/1427247692705959881058285969449495136382746624*x(11)+206796938269122258779026599337/91343852333181432387730302044767688728495783936*x(12);
 
equa2sub =x(2)+2179336774425063/9007199254740992+(37526423397676813332334898889027/855220629711474430592113990172672+49532669641878859065350990413901/427610314855737215296056995086336*i)*x(7)-7398539084151252801240731883817/7245856949184205584664105964273664*x(8)+9701869628173919811376223237191/75261204389257980309851363976180400128*x(9)-1277211448906621552448654388595/23860751773952951312363398400278311993344*x(10)+1362802704850279953288683880255/70907773931469299065694310054832901202116608*x(11)-8625402993825599933615303699537/3702438626946186324992873082646789575845217304576*x(12);
 
equa3sub =x(3)-2179336774425063/36028797018963968-(12508807799225604444111632963009/1048697196988140797536670555570176+49532669641878859065350990413901/1573045795482211196305005833355264*i)*x(7)-7398539084151252801240731883817/86588217623736540910447134758666240*x(8)-29105608884521759434128669711573/75649093851100752735482115538246696960*x(9)+1277211448906621552448654388595/17711241862742021199068701875804540239872*x(10)-1362802704850279953288683880255/61068558073531812431847844722400210020466688*x(11)+8625402993825599933615303699537/3380027201713290762974992106633635151204912726016*x(12);

equa4sub =x(4)+7748752975733557/288230376151711744+(33356820797934943209001720132433/6190408764194964734552061289431040+22014519840835049131921318329153/1547602191048741183638015322357760*i)*x(7)+26305916743648898510433925203569/863922993464667543602663285577482240*x(8)-51743304683594236328831377155201/310355742240037684763822436037613846528*x(9)-36329570102232795753818397281155/212254113490217598493003436507731431784448*x(10)+19382082913426203433050528326643/635304746339119300790994312862157102563459072*x(11)-2555674961133510611575096049613/842274022614853767674660051874414976259181248512*x(12);

equa5sub =x(5)-2179336774425063/144115188075855872-(37526423397676813332334898889027/12309575435976212511299345462591488+49532669641878859065350990413901/6154787717988106255649672731295744*i)*x(7)-7398539084151252801240731883817/461924515915419508444148023940874240*x(8)+29105608884521759434128669711573/524888983415592000040805790022931316736*x(9)-1277211448906621552448654388595/6886797782101713761219919597640643248128*x(10)-151422522761142217032075986695/2412410515753537353989004504838094190542848*x(11)+8625402993825599933615303699537/2090381500781707541347807227300837103175632683008*x(12);
 
equa6sub =x(6)+5579102142528161/576460752303423488+(37526423397676813332334898889027/19182188319735057694389731174907904+49532669641878859065350990413901/9591094159867528847194865587453952*i)*x(7)+7398539084151252801240731883817/743426739634181641860703322279772160*x(8)-29105608884521759434128669711573/975292541365611677959817308065299955712*x(9)+1277211448906621552448654388595/25335327515734513772510566088095356157952*x(10)-454267568283426651096227960085/2601984310676884475399766100960607803015168*x(11)-8625402993825599933615303699537/1123147225083019881738503323981193479786657218560*x(12);

equa7sub =x(7)+(2322028850419079/1125899906842624+2562706364895407/9007199254740992*i)*(-5318998413755481/4503599627370496-11316947028382809420225314005533/13362822339241787978001781096448*x(2)+47539893266487660052480027409623/49157681108819099884531432292352*x(3)-9653174320626376094416784221761/9672513694054632397737595764736*x(4)+48624853531325315583340957398461/48084279046782080122263068213248*x(5)-19076967537554081507840067761767/18732605780991267279677471850496*x(6));
 
equa8sub =x(8)+1828304033752709/70368744177664+12781645729332806833062081373649/13820375345581446809128009728*x(2)+41947465506445508270841202315/129026498829925866291593216*x(3)-106470105689011260713633181571/402295493271512698197114880*x(4)+143015982726173118919053113709/573600972587142771040583680*x(5)-21546008834667373653917509482703/88623373464844422562206187520*x(6);
 
equa9sub =x(9)-8744181223955479/549755813888-53428943499171695984835881591627/410697999846477507034349568*x(2)+56110677749960030092146867614297/34401225025749569220116480*x(3)+28483769964134474313932345620805/17641681452007428831838208*x(4)-14347810331846682779060483651413/14918242169858103808360448*x(5)+22516280630792217615492161016547/27719481220333695943049216*x(6);
 
equa10sub =x(10)+2143354288027763/268435456+76889959165422172751349313276095/1324537800215405753532416*x(2)-40374630662549725282540084069465/122896428192007114981376*x(3)+40991188782415858629190320752825/23012637096507873427456*x(4)+13765354859219285845701862029855/3982229928972283543552*x(5)-64806667879765933354102588502575/43949787413105820565504*x(6);
 
equa11sub =x(11)-1743625504902557/524288-683191558149789503090357463411/29326767937702191104*x(2)+22959445633915007586210679339785/202058909099976753152*x(3)-11655028849494739207651118904051/32844485577164910592*x(4)+652317456398320801335468445423/498874802037594112*x(5)+383885133922523724333435256089/67259717998721024*x(6);
 
equa12sub =x(12)+3878949580580463/8192+19055803659565858140764297628659/5841418173556017152*x(2)-10006131399781328118029811914599/666592829503797504*x(3)+20317868644705667433246067365239/498327785943072384*x(4)-5117246172621763207417567132397/51531882592622344*x(5)+16061175637909210839969990512723/55375433542216160*x(6);
 

F(1)=equa1sub;
F(2)=equa2sub;
F(3)=equa3sub;
F(4)=equa4sub;
F(5)=equa5sub;
F(6)=equa6sub;

F(7)=equa7sub;
F(8)=equa8sub;
F(9)=equa9sub;
F(10)=equa10sub;
F(11)=equa11sub;
F(12)=equa12sub;
 

Answer 1

[Walter Roberson]

No. Your numeric constants cannot possibly be represented precisely. It is not possible to get correct solutions for those equations in the form written.

[dcydhb dcydhb]

It's a fraction, not a decimal. why can't be precisely solved?

and if a Remove all assignments?

when i Removed all assignments,why in my results there are still Fraction?

equa1sub =
 
x(1)-2/d*(1/6*d^2-1/4*a^2)-4*x(7)/d/((2*m0+sinh(2*m0))/m0)^(1/2)/m0*sinh(m0*d)*(besselj(0,m0*a)+i*bessely(0,m0*a))-4*x(8)/d/((2*m1+sin(2*m1))/m1)^(1/2)/m1*sin(d*m1)*besselk(0,m1*a)-4*x(9)/d/((2*m2+sin(2*m2))/m2)^(1/2)/m2*sin(d*m2)*besselk(0,m2*a)-4*x(10)/d/((2*m3+sin(2*m3))/m3)^(1/2)/m3*sin(d*m3)*besselk(0,m3*a)-4*x(11)/d/((2*m4+sin(2*m4))/m4)^(1/2)/m4*sin(d*m4)*besselk(0,m4*a)-4*x(12)/d/((2*m5+sin(2*m5))/m5)^(1/2)/m5*sin(d*m5)*besselk(0,m5*a)
 
 
 
equa2sub =
 
x(2)[phone]/2778046668940015*d+2*x(7)*d*2^(1/2)*m0*(exp(m0*d)^2-1)/exp(m0*d)/((4*exp(m0)^2*m0+exp(m0)^4-1)/exp(m0)^2/m0)^(1/2)/(m0^2*d^2+2778046668940015/281474976710656)*(besselj(0,m0*a)+i*bessely(0,m0*a))+2*x(8)*d*sin(d*m1)*m1*2^(1/2)/((m1+sin(m1)*cos(m1))/m1)^(1/2)/(-2778046668940015/281474976710656+d^2*m1^2)*besselk(0,m1*a)+2*x(9)*d*sin(d*m2)*m2*2^(1/2)/((m2+sin(m2)*cos(m2))/m2)^(1/2)/(-2778046668940015/281474976710656+d^2*m2^2)*besselk(0,m2*a)+2*x(10)*d*sin(d*m3)*m3*2^(1/2)/((m3+sin(m3)*cos(m3))/m3)^(1/2)/(-2778046668940015/281474976710656+d^2*m3^2)*besselk(0,m3*a)+2*x(11)*d*sin(d*m4)*m4*2^(1/2)/((m4+sin(m4)*cos(m4))/m4)^(1/2)/(-2778046668940015/281474976710656+d^2*m4^2)*besselk(0,m4*a)+2*x(12)*d*sin(d*m5)*m5*2^(1/2)/((m5+sin(m5)*cos(m5))/m5)^(1/2)/(-2778046668940015/281474976710656+d^2*m5^2)*besselk(0,m5*a)
 
 
 
equa3sub =
 
x(3)-140737488355328/2778046668940015*d-2*x(7)*d*2^(1/2)*m0*(exp(m0*d)^2-1)/exp(m0*d)/((4*exp(m0)^2*m0+exp(m0)^4-1)/exp(m0)^2/m0)^(1/2)/(m0^2*d^2+2778046668940015/70368744177664)*(besselj(0,m0*a)+i*bessely(0,m0*a))-2*x(8)*d*sin(d*m1)*m1*2^(1/2)/((m1+sin(m1)*cos(m1))/m1)^(1/2)/(-2778046668940015/70368744177664+d^2*m1^2)*besselk(0,m1*a)-2*x(9)*d*sin(d*m2)*m2*2^(1/2)/((m2+sin(m2)*cos(m2))/m2)^(1/2)/(-2778046668940015/70368744177664+d^2*m2^2)*besselk(0,m2*a)-2*x(10)*d*sin(d*m3)*m3*2^(1/2)/((m3+sin(m3)*cos(m3))/m3)^(1/2)/(-2778046668940015/70368744177664+d^2*m3^2)*besselk(0,m3*a)-2*x(11)*d*sin(d*m4)*m4*2^(1/2)/((m4+sin(m4)*cos(m4))/m4)^(1/2)/(-2778046668940015/70368744177664+d^2*m4^2)*besselk(0,m4*a)-2*x(12)*d*sin(d*m5)*m5*2^(1/2)/((m5+sin(m5)*cos(m5))/m5)^(1/2)/(-2778046668940015/70368744177664+d^2*m5^2)*besselk(0,m5*a)
 
 
 
equa4sub =
 
x(4)[phone]/25002420020460135*d+2*x(7)*d*2^(1/2)*m0*(exp(m0*d)^2-1)/exp(m0*d)/((4*exp(m0)^2*m0+exp(m0)^4-1)/exp(m0)^2/m0)^(1/2)/(m0^2*d^2+3125302502557517/35184372088832)*(besselj(0,m0*a)+i*bessely(0,m0*a))+2*x(8)*d*sin(d*m1)*m1*2^(1/2)/((m1+sin(m1)*cos(m1))/m1)^(1/2)/(-3125302502557517/35184372088832+d^2*m1^2)*besselk(0,m1*a)+2*x(9)*d*sin(d*m2)*m2*2^(1/2)/((m2+sin(m2)*cos(m2))/m2)^(1/2)/(-3125302502557517/35184372088832+d^2*m2^2)*besselk(0,m2*a)+2*x(10)*d*sin(d*m3)*m3*2^(1/2)/((m3+sin(m3)*cos(m3))/m3)^(1/2)/(-3125302502557517/35184372088832+d^2*m3^2)*besselk(0,m3*a)+2*x(11)*d*sin(d*m4)*m4*2^(1/2)/((m4+sin(m4)*cos(m4))/m4)^(1/2)/(-3125302502557517/35184372088832+d^2*m4^2)*besselk(0,m4*a)+2*x(12)*d*sin(d*m5)*m5*2^(1/2)/((m5+sin(m5)*cos(m5))/m5)^(1/2)/(-3125302502557517/35184372088832+d^2*m5^2)*besselk(0,m5*a)
 
 
 
equa5sub =
 
x(5)-35184372088832/2778046668940015*d-2*x(7)*d*2^(1/2)*m0*(exp(m0*d)^2-1)/((4*exp(m0)^2*m0+exp(m0)^4-1)/exp(m0)^2/m0)^(1/2)/exp(m0*d)/(m0^2*d^2+2778046668940015/17592186044416)*(besselj(0,m0*a)+i*bessely(0,m0*a))-2*x(8)*d*sin(d*m1)*m1*2^(1/2)/((m1+sin(m1)*cos(m1))/m1)^(1/2)/(-2778046668940015/17592186044416+d^2*m1^2)*besselk(0,m1*a)-2*x(9)*d*sin(d*m2)*m2*2^(1/2)/((m2+sin(m2)*cos(m2))/m2)^(1/2)/(-2778046668940015/17592186044416+d^2*m2^2)*besselk(0,m2*a)-2*x(10)*d*sin(d*m3)*m3*2^(1/2)/((m3+sin(m3)*cos(m3))/m3)^(1/2)/(-2778046668940015/17592186044416+d^2*m3^2)*besselk(0,m3*a)-2*x(11)*d*sin(d*m4)*m4*2^(1/2)/((m4+sin(m4)*cos(m4))/m4)^(1/2)/(-2778046668940015/17592186044416+d^2*m4^2)*besselk(0,m4*a)-2*x(12)*d*sin(d*m5)*m5*2^(1/2)/((m5+sin(m5)*cos(m5))/m5)^(1/2)/(-2778046668940015/17592186044416+d^2*m5^2)*besselk(0,m5*a)
 
 
 
equa6sub =
 
x(6)[phone]/69451166723500375*d+2*x(7)*d*2^(1/2)*m0*(exp(m0*d)^2-1)/((4*exp(m0)^2*m0+exp(m0)^4-1)/exp(m0)^2/m0)^(1/2)/exp(m0*d)/(m0^2*d^2+8681395840437547/35184372088832)*(besselj(0,m0*a)+i*bessely(0,m0*a))+2*x(8)*d*sin(d*m1)*m1*2^(1/2)/((m1+sin(m1)*cos(m1))/m1)^(1/2)/(-8681395840437547/35184372088832+d^2*m1^2)*besselk(0,m1*a)+2*x(9)*d*sin(d*m2)*m2*2^(1/2)/((m2+sin(m2)*cos(m2))/m2)^(1/2)/(-8681395840437547/35184372088832+d^2*m2^2)*besselk(0,m2*a)+2*x(10)*d*sin(d*m3)*m3*2^(1/2)/((m3+sin(m3)*cos(m3))/m3)^(1/2)/(-8681395840437547/35184372088832+d^2*m3^2)*besselk(0,m3*a)+2*x(11)*d*sin(d*m4)*m4*2^(1/2)/((m4+sin(m4)*cos(m4))/m4)^(1/2)/(-8681395840437547/35184372088832+d^2*m4^2)*besselk(0,m4*a)+2*x(12)*d*sin(d*m5)*m5*2^(1/2)/((m5+sin(m5)*cos(m5))/m5)^(1/2)/(-8681395840437547/35184372088832+d^2*m5^2)*besselk(0,m5*a)
 
 
 
equa7sub =
 
x(7)-(-1/4*a*2^(1/2)*(exp(m0*d)^2-1)/d/((m0+sinh(m0)*cosh(m0))/m0)^(1/2)/m0/exp(m0*d)+4*x(1)/d/((2*m0+sinh(2*m0))/m0)^(1/2)/m0*sinh(m0*d)*s0-2*x(2)*d*2^(1/2)*m0*(exp(m0*d)^2-1)/exp(m0*d)/((4*exp(m0)^2*m0+exp(m0)^4-1)/exp(m0)^2/m0)^(1/2)/(m0^2*d^2+2778046668940015/281474976710656)*s1+2*x(3)*d*2^(1/2)*m0*(exp(m0*d)^2-1)/exp(m0*d)/((4*exp(m0)^2*m0+exp(m0)^4-1)/exp(m0)^2/m0)^(1/2)/(m0^2*d^2+2778046668940015/70368744177664)*s2-2*x(4)*d*2^(1/2)*m0*(exp(m0*d)^2-1)/exp(m0*d)/((4*exp(m0)^2*m0+exp(m0)^4-1)/exp(m0)^2/m0)^(1/2)/(m0^2*d^2+3125302502557517/35184372088832)*s3+2*x(5)*d*2^(1/2)*m0*(exp(m0*d)^2-1)/((4*exp(m0)^2*m0+exp(m0)^4-1)/exp(m0)^2/m0)^(1/2)/exp(m0*d)/(m0^2*d^2+2778046668940015/17592186044416)*s4-2*x(6)*d*2^(1/2)*m0*(exp(m0*d)^2-1)/((4*exp(m0)^2*m0+exp(m0)^4-1)/exp(m0)^2/m0)^(1/2)/exp(m0*d)/(m0^2*d^2+8681395840437547/35184372088832)*s5)/(-besselj(1,m0*a)*m0-i*bessely(1,m0*a)*m0)/m0
 
 
 
equa8sub =
 
x(8)+(-1/2*sin(d*m1)/d*a*2^(1/2)/((m1+sin(m1)*cos(m1))/m1)^(1/2)/m1+4*x(1)/d/((2*m1+sin(2*m1))/m1)^(1/2)/m1*sin(d*m1)*s0-2*x(2)*d*sin(d*m1)*m1*2^(1/2)/((m1+sin(m1)*cos(m1))/m1)^(1/2)/(-2778046668940015/281474976710656+d^2*m1^2)*s1+2*x(3)*d*sin(d*m1)*m1*2^(1/2)/((m1+sin(m1)*cos(m1))/m1)^(1/2)/(-2778046668940015/70368744177664+d^2*m1^2)*s2-2*x(4)*d*sin(d*m1)*m1*2^(1/2)/((m1+sin(m1)*cos(m1))/m1)^(1/2)/(-3125302502557517/35184372088832+d^2*m1^2)*s3+2*x(5)*d*sin(d*m1)*m1*2^(1/2)/((m1+sin(m1)*cos(m1))/m1)^(1/2)/(-2778046668940015/17592186044416+d^2*m1^2)*s4-2*x(6)*d*sin(d*m1)*m1*2^(1/2)/((m1+sin(m1)*cos(m1))/m1)^(1/2)/(-8681395840437547/35184372088832+d^2*m1^2)*s5)/besselk(1,m1*a)/m1^2
 
 
 
equa9sub =
 
x(9)+(-1/2*sin(d*m2)/d*a*2^(1/2)/((m2+sin(m2)*cos(m2))/m2)^(1/2)/m2+4*x(1)/d/((2*m2+sin(2*m2))/m2)^(1/2)/m2*sin(d*m2)*s0-2*x(2)*d*sin(d*m2)*m2*2^(1/2)/((m2+sin(m2)*cos(m2))/m2)^(1/2)/(-2778046668940015/281474976710656+d^2*m2^2)*s1+2*x(3)*d*sin(d*m2)*m2*2^(1/2)/((m2+sin(m2)*cos(m2))/m2)^(1/2)/(-2778046668940015/70368744177664+d^2*m2^2)*s2-2*x(4)*d*sin(d*m2)*m2*2^(1/2)/((m2+sin(m2)*cos(m2))/m2)^(1/2)/(-3125302502557517/35184372088832+d^2*m2^2)*s3+2*x(5)*d*sin(d*m2)*m2*2^(1/2)/((m2+sin(m2)*cos(m2))/m2)^(1/2)/(-2778046668940015/17592186044416+d^2*m2^2)*s4-2*x(6)*d*sin(d*m2)*m2*2^(1/2)/((m2+sin(m2)*cos(m2))/m2)^(1/2)/(-8681395840437547/35184372088832+d^2*m2^2)*s5)/besselk(1,m2*a)/m2^2
 
 
 
equa10sub =
 
x(10)+(-1/2*sin(d*m3)/d*a*2^(1/2)/((m3+sin(m3)*cos(m3))/m3)^(1/2)/m3+4*x(1)/d/((2*m3+sin(2*m3))/m3)^(1/2)/m3*sin(d*m3)*s0-2*x(2)*d*sin(d*m3)*m3*2^(1/2)/((m3+sin(m3)*cos(m3))/m3)^(1/2)/(-2778046668940015/281474976710656+d^2*m3^2)*s1+2*x(3)*d*sin(d*m3)*m3*2^(1/2)/((m3+sin(m3)*cos(m3))/m3)^(1/2)/(-2778046668940015/70368744177664+d^2*m3^2)*s2-2*x(4)*d*sin(d*m3)*m3*2^(1/2)/((m3+sin(m3)*cos(m3))/m3)^(1/2)/(-3125302502557517/35184372088832+d^2*m3^2)*s3+2*x(5)*d*sin(d*m3)*m3*2^(1/2)/((m3+sin(m3)*cos(m3))/m3)^(1/2)/(-2778046668940015/17592186044416+d^2*m3^2)*s4-2*x(6)*d*sin(d*m3)*m3*2^(1/2)/((m3+sin(m3)*cos(m3))/m3)^(1/2)/(-8681395840437547/35184372088832+d^2*m3^2)*s5)/besselk(1,m3*a)/m3^2
 
 
 
equa11sub =
 
x(11)+(-1/2*sin(d*m4)/d*a*2^(1/2)/((m4+sin(m4)*cos(m4))/m4)^(1/2)/m4+4*x(1)/d/((2*m4+sin(2*m4))/m4)^(1/2)/m4*sin(d*m4)*s0-2*x(2)*d*sin(d*m4)*m4*2^(1/2)/((m4+sin(m4)*cos(m4))/m4)^(1/2)/(-2778046668940015/281474976710656+d^2*m4^2)*s1+2*x(3)*d*sin(d*m4)*m4*2^(1/2)/((m4+sin(m4)*cos(m4))/m4)^(1/2)/(-2778046668940015/70368744177664+d^2*m4^2)*s2-2*x(4)*d*sin(d*m4)*m4*2^(1/2)/((m4+sin(m4)*cos(m4))/m4)^(1/2)/(-3125302502557517/35184372088832+d^2*m4^2)*s3+2*x(5)*d*sin(d*m4)*m4*2^(1/2)/((m4+sin(m4)*cos(m4))/m4)^(1/2)/(-2778046668940015/17592186044416+d^2*m4^2)*s4-2*x(6)*d*sin(d*m4)*m4*2^(1/2)/((m4+sin(m4)*cos(m4))/m4)^(1/2)/(-8681395840437547/35184372088832+d^2*m4^2)*s5)/besselk(1,m4*a)/m4^2
 
 
 
equa12sub =
 
x(12)+(-1/2*sin(d*m5)/d*a*2^(1/2)/((m5+sin(m5)*cos(m5))/m5)^(1/2)/m5+4*x(1)/d/((2*m5+sin(2*m5))/m5)^(1/2)/m5*sin(d*m5)*s0-2*x(2)*d*sin(d*m5)*m5*2^(1/2)/((m5+sin(m5)*cos(m5))/m5)^(1/2)/(-2778046668940015/281474976710656+d^2*m5^2)*s1+2*x(3)*d*sin(d*m5)*m5*2^(1/2)/((m5+sin(m5)*cos(m5))/m5)^(1/2)/(-2778046668940015/70368744177664+d^2*m5^2)*s2-2*x(4)*d*sin(d*m5)*m5*2^(1/2)/((m5+sin(m5)*cos(m5))/m5)^(1/2)/(-3125302502557517/35184372088832+d^2*m5^2)*s3+2*x(5)*d*sin(d*m5)*m5*2^(1/2)/((m5+sin(m5)*cos(m5))/m5)^(1/2)/(-2778046668940015/17592186044416+d^2*m5^2)*s4-2*x(6)*d*sin(d*m5)*m5*2^(1/2)/((m5+sin(m5)*cos(m5))/m5)^(1/2)/(-8681395840437547/35184372088832+d^2*m5^2)*s5)/besselk(1,m5*a)/m5^2
 
 
>> 

[Torsten]

Write you equations as

A*x=b

and solve for x using

x=A\b.

Or - if it's too much work for you to construct A and b - use "fsolve".

Best wishes

Torsten.

[Walter Roberson]

It's a fraction, not a decimal. why can't be precisely solved?

When you have a integer or floating point number inside a regular MATLAB expression, MATLAB treats the number as being double precision and uses the double precision representation of it -- unless, that is, the number is one of the forms int8(N) uint8(N) int16(N) uint16(N) int32(N) uint32(N) int64(N) uint64(N), where N is a literal number. For example int16(12345) . In those special cases, then MATLAB recognizes the number as being the given type at parse time rather than at execution time. For example, uint64(12345678901234567) is the 64 bit integer that is exactly 12345678901234567 but uint64(0+12345678901234567) is not one of the magic forms, so this is handled at execution time, so the number 12345678901234567 is to be parsed as a floating point number, and 0 floating point is to be added to it, and the result is to be converted to uint64 -- which gives you the 64 bit integer 12345678901234568 . In practice the only time it makes a difference whether the number is handled at parsing time or at execution time is if the number exceeds 9007199254740992 which is the maximum double precision number representable exactly as an integer, after which the integers start being separated by 2 or more. uint64(1+9007199254740992) is uint64 9007199254740992 not uint64 9007199254740993 for example.

Now, whether the numbers are treated as double precision or not matters because you do have values that exceed 9007199254740992 . You also have values that exceed 18446744073709551615 which is the largest uin64 .

In your expression 4154756651791824122955846205623 / 10141204801825835211973625643008 neither are surrounded by uint64() or similar, so both of them will be translated into double precision floating point as they are encountered. The first of them is approximated as 4154756651791824311205918408704 . The second of them is approximated as itself, as it just happens to be exactly 2^103 . The result after floating point approximation is 0.4096906366631898332997252509812824428081512451171875 exactly, which is exactly equal to 1845082598613523 / 4503599627370496.

coding uint64(4154756651791824122955846205623) / uint64(10141204801825835211973625643008) is not going to help. Each of them overflows intmax('uint64') so each of them would "saturate" to be stored as intmax('uint64') . You would then be doing integer division of two values that have saturated to the same value, so you would get the uint64 result exactly equal to 1.

In order to use the full precision of 154756651791824122955846205623 / 10141204801825835211973625643008 you cannot code them in numeric form. You have to instead code them as symbolic numbers using sym() and quoted strings,

sym('154756651791824122955846205623') / sym('10141204801825835211973625643008')

However, we know from past discussions that this is not acceptable to you even though it is the only way to get accurate results from those inputs.

MATLAB (with the symbolic toolbox) can give you exact results if you are willing to code your constants in symbolic form. But you are not willing to do so.

I find it implausible in the extreme that you just happened to have physical constants known to over 108 bits of precision. I think you generated those constants out of other symbolic code, based upon constants that you had originally coded as floating point. I believe the expressions you present are output of some symbolic work -- and that being the case, you should be leaving them as symbolic instead of converting them to numeric code.

[Walter Roberson]

My tests suggest that it is not practical to solve in the general sense, with the (-1/2*sin(d*m3)/d*a*2^(1/2) etc. terms. You can reframe it as solving a 12 x 12 symbolic matrix for the general solution, and then substituting terms from the equations into the general solution, but it turns out not to be practical to solve 12 x 12 in the general case.

Answer 2

[John D'Errico]

Without trying to read every one of those equations, are they not just 12 linear equations in 12 unknowns? I can't find anything that is not linear in the variables.

If so, then write them as a matrix problem of the form A*x = b. Then use backslash...

x = A\b;

If you need to convert the problem to a matrix form, then if they are linear, this will do it.

help equationsToMatrix

If the values m1, m2, etc. are not known, then you will need to do this in fully symbolic form. If they are known, then convert A to a double first. If you leave it fully symbolic however, expect the solution be fairly computationally intensive. That may be excluded by your desire for an "effective" solution. But you cannot always have everything you want.

[dcydhb dcydhb]

the values m1, m2, etc. are all known except for the 12 variables,i was wondering how to solve the 12 root in a symbolic way without assigning them,and after get the root that i assign them,and this problem we can use

help equationsToMatrix

but if the equations are nolinear?

[dcydhb dcydhb]

i have used the

help equationsToMatrix

method,

codes are as this

syms alpha0 alpha1 alpha2 alpha3 alpha4 alpha5 a0 a1 a2  a3 a4 a5;

equa1 =alpha0 + (2*(a^2/4 - d^2/6))/d - (2*a1*sin(d*m1)*besselk(0, a*m1))/(d*m1*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*a2*sin(d*m2)*besselk(0, a*m2))/(d*m2*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*a3*sin(d*m3)*besselk(0, a*m3))/(d*m3*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*a4*sin(d*m4)*besselk(0, a*m4))/(d*m4*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*a5*sin(d*m5)*besselk(0, a*m5))/(d*m5*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*a0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/(d*m0*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));
 
equa2 =alpha1 + (2*d)/pi^2 - (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((sin(2*m1)/(4*m1) + 1/2)^(1/2)*(- d^2*m1^2 + pi^2)) - (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((sin(2*m2)/(4*m2) + 1/2)^(1/2)*(- d^2*m2^2 + pi^2)) - (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((sin(2*m3)/(4*m3) + 1/2)^(1/2)*(- d^2*m3^2 + pi^2)) - (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((sin(2*m4)/(4*m4) + 1/2)^(1/2)*(- d^2*m4^2 + pi^2)) - (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((sin(2*m5)/(4*m5) + 1/2)^(1/2)*(- d^2*m5^2 + pi^2)) + (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((sinh(2*m0)/(4*m0) + 1/2)^(1/2)*(d^2*m0^2 + pi^2));
 
equa3 =alpha2 - d/(2*pi^2) + (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 4*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 4*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 4*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 4*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 4*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 4*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));
 
equa4 =alpha3 + (2*d)/(9*pi^2) - (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 9*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 9*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 9*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 9*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 9*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 9*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));
 
equa5 =alpha4 - d/(8*pi^2) + (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 16*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 16*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 16*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 16*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 16*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 16*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));
 
equa6 =alpha5 + (2*d)/(25*pi^2) - (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 25*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 25*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 25*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 25*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 25*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 25*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));
 
equa7 =a0 - ((a*sinh(d*m0))/(2*d*m0*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) - (2*alpha0*s0*sinh(d*m0))/(d*m0*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) + (2*alpha1*d*m0*s1*sinh(d*m0))/((sinh(2*m0)/(4*m0) + 1/2)^(1/2)*(d^2*m0^2 + pi^2)) - (2*alpha2*d*m0*s2*sinh(d*m0))/((d^2*m0^2 + 4*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) + (2*alpha3*d*m0*s3*sinh(d*m0))/((d^2*m0^2 + 9*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) - (2*alpha4*d*m0*s4*sinh(d*m0))/((d^2*m0^2 + 16*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) + (2*alpha5*d*m0*s5*sinh(d*m0))/((d^2*m0^2 + 25*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)))/(m0*(m0*besselj(1, a*m0) + m0*bessely(1, a*m0)*i));
 
equa8 =a1 + ((2*alpha0*s0*sin(d*m1))/(d*m1*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (a*sin(d*m1))/(2*d*m1*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*alpha1*d*m1*s1*sin(d*m1))/((sin(2*m1)/(4*m1) + 1/2)^(1/2)*(- d^2*m1^2 + pi^2)) - (2*alpha2*d*m1*s2*sin(d*m1))/((- d^2*m1^2 + 4*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*alpha3*d*m1*s3*sin(d*m1))/((- d^2*m1^2 + 9*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*alpha4*d*m1*s4*sin(d*m1))/((- d^2*m1^2 + 16*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*alpha5*d*m1*s5*sin(d*m1))/((- d^2*m1^2 + 25*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)))/(m1^2*besselk(1, a*m1));
 
equa9 =a2 + ((2*alpha0*s0*sin(d*m2))/(d*m2*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (a*sin(d*m2))/(2*d*m2*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*alpha1*d*m2*s1*sin(d*m2))/((sin(2*m2)/(4*m2) + 1/2)^(1/2)*(- d^2*m2^2 + pi^2)) - (2*alpha2*d*m2*s2*sin(d*m2))/((- d^2*m2^2 + 4*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*alpha3*d*m2*s3*sin(d*m2))/((- d^2*m2^2 + 9*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*alpha4*d*m2*s4*sin(d*m2))/((- d^2*m2^2 + 16*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*alpha5*d*m2*s5*sin(d*m2))/((- d^2*m2^2 + 25*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)))/(m2^2*besselk(1, a*m2)); 
 
equa10 =a3 + ((2*alpha0*s0*sin(d*m3))/(d*m3*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (a*sin(d*m3))/(2*d*m3*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*alpha1*d*m3*s1*sin(d*m3))/((sin(2*m3)/(4*m3) + 1/2)^(1/2)*(- d^2*m3^2 + pi^2)) - (2*alpha2*d*m3*s2*sin(d*m3))/((- d^2*m3^2 + 4*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*alpha3*d*m3*s3*sin(d*m3))/((- d^2*m3^2 + 9*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*alpha4*d*m3*s4*sin(d*m3))/((- d^2*m3^2 + 16*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*alpha5*d*m3*s5*sin(d*m3))/((- d^2*m3^2 + 25*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)))/(m3^2*besselk(1, a*m3));
 
equa11 =a4 + ((2*alpha0*s0*sin(d*m4))/(d*m4*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (a*sin(d*m4))/(2*d*m4*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*alpha1*d*m4*s1*sin(d*m4))/((sin(2*m4)/(4*m4) + 1/2)^(1/2)*(- d^2*m4^2 + pi^2)) - (2*alpha2*d*m4*s2*sin(d*m4))/((- d^2*m4^2 + 4*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*alpha3*d*m4*s3*sin(d*m4))/((- d^2*m4^2 + 9*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*alpha4*d*m4*s4*sin(d*m4))/((- d^2*m4^2 + 16*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*alpha5*d*m4*s5*sin(d*m4))/((- d^2*m4^2 + 25*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)))/(m4^2*besselk(1, a*m4));
 
equa12 =a5 + ((2*alpha0*s0*sin(d*m5))/(d*m5*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (a*sin(d*m5))/(2*d*m5*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*alpha1*d*m5*s1*sin(d*m5))/((sin(2*m5)/(4*m5) + 1/2)^(1/2)*(- d^2*m5^2 + pi^2)) - (2*alpha2*d*m5*s2*sin(d*m5))/((- d^2*m5^2 + 4*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*alpha3*d*m5*s3*sin(d*m5))/((- d^2*m5^2 + 9*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*alpha4*d*m5*s4*sin(d*m5))/((- d^2*m5^2 + 16*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*alpha5*d*m5*s5*sin(d*m5))/((- d^2*m5^2 + 25*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)))/(m5^2*besselk(1, a*m5));
 



[A, b] = equationsToMatrix([equa1,equa2,equa3,equa4,equa5,equa6,equa7,equa8,equa9,equa10,equa11,equa12,], [alpha0, alpha1,alpha2, alpha3, alpha4,alpha5,a0,a1,a2 ,a3,a4,a5])


x = A\b

and

syms alpha0 alpha1 alpha2 alpha3 alpha4 alpha5 a0 a1 a2  a3 a4 a5;

are 12 unknown variables and it seems that it can.t run out a result.

[Torsten]

equa1 to equa12 are expressions, not equations (they lack the == 0).

And of course you should assign numerical values to the variables not solved for .

[dcydhb dcydhb]

even i added == 0).may be it can't run out a result but when a assigned the values,i run out the root precisely.

[Torsten]

This works for me in Octave:

syms a b c d e f g h k l m n 
equa1sub =a+484533722967603/281474976710656-(4154756651791824122955846205623/10141204801825835211973625643008+10968068365840776354319913193387/10141204801825835211973625643008*i)*g+15954949269969134648023144147861/83076749736557242056487941267521536*h-71813660819499486824121496911249/680564733841876926926749214863536422912*k+68704458373558018815486967994675/1393796574908163946345982392040522594123776*l-26218118780833903306440628355937/1427247692705959881058285969449495136382746624*m+206796938269122258779026599337/91343852333181432387730302044767688728495783936*n==0;
equa2sub =b+2179336774425063/9007199254740992+(37526423397676813332334898889027/855220629711474430592113990172672+49532669641878859065350990413901/427610314855737215296056995086336*i)*g-7398539084151252801240731883817/7245856949184205584664105964273664*h+9701869628173919811376223237191/75261204389257980309851363976180400128*k-1277211448906621552448654388595/23860751773952951312363398400278311993344*l+1362802704850279953288683880255/70907773931469299065694310054832901202116608*m-8625402993825599933615303699537/3702438626946186324992873082646789575845217304576*n==0; 
equa3sub =c-2179336774425063/36028797018963968-(12508807799225604444111632963009/1048697196988140797536670555570176+49532669641878859065350990413901/1573045795482211196305005833355264*i)*g-7398539084151252801240731883817/86588217623736540910447134758666240*h-29105608884521759434128669711573/75649093851100752735482115538246696960*k+1277211448906621552448654388595/17711241862742021199068701875804540239872*l-1362802704850279953288683880255/61068558073531812431847844722400210020466688*m+8625402993825599933615303699537/3380027201713290762974992106633635151204912726016*n==0;
equa4sub =d+7748752975733557/288230376151711744+(33356820797934943209001720132433/6190408764194964734552061289431040+22014519840835049131921318329153/1547602191048741183638015322357760*i)*g+26305916743648898510433925203569/863922993464667543602663285577482240*h-51743304683594236328831377155201/310355742240037684763822436037613846528*k-36329570102232795753818397281155/212254113490217598493003436507731431784448*l+19382082913426203433050528326643/635304746339119300790994312862157102563459072*m-2555674961133510611575096049613/842274022614853767674660051874414976259181248512*n==0;
equa5sub =e-2179336774425063/144115188075855872-(37526423397676813332334898889027/12309575435976212511299345462591488+49532669641878859065350990413901/6154787717988106255649672731295744*i)*g-7398539084151252801240731883817/461924515915419508444148023940874240*h+29105608884521759434128669711573/524888983415592000040805790022931316736*k-1277211448906621552448654388595/6886797782101713761219919597640643248128*l-151422522761142217032075986695/2412410515753537353989004504838094190542848*m+8625402993825599933615303699537/2090381500781707541347807227300837103175632683008*n==0; 
equa6sub =f+5579102142528161/576460752303423488+(37526423397676813332334898889027/19182188319735057694389731174907904+49532669641878859065350990413901/9591094159867528847194865587453952*i)*g+7398539084151252801240731883817/743426739634181641860703322279772160*h-29105608884521759434128669711573/975292541365611677959817308065299955712*k+1277211448906621552448654388595/25335327515734513772510566088095356157952*l-454267568283426651096227960085/2601984310676884475399766100960607803015168*m-8625402993825599933615303699537/1123147225083019881738503323981193479786657218560*n==0;
equa7sub =g+(2322028850419079/1125899906842624+2562706364895407/9007199254740992*i)*(-5318998413755481/4503599627370496-11316947028382809420225314005533/13362822339241787978001781096448*b+47539893266487660052480027409623/49157681108819099884531432292352*c-9653174320626376094416784221761/9672513694054632397737595764736*d+48624853531325315583340957398461/48084279046782080122263068213248*e-19076967537554081507840067761767/18732605780991267279677471850496*f)==0; 
equa8sub =h+1828304033752709/70368744177664+12781645729332806833062081373649/13820375345581446809128009728*b+41947465506445508270841202315/129026498829925866291593216*c-106470105689011260713633181571/402295493271512698197114880*d+143015982726173118919053113709/573600972587142771040583680*e-21546008834667373653917509482703/88623373464844422562206187520*f==0; 
equa9sub =k-8744181223955479/549755813888-53428943499171695984835881591627/410697999846477507034349568*b+56110677749960030092146867614297/34401225025749569220116480*c+28483769964134474313932345620805/17641681452007428831838208*d-14347810331846682779060483651413/14918242169858103808360448*e+22516280630792217615492161016547/27719481220333695943049216*f==0; 
equa10sub =l+2143354288027763/268435456+76889959165422172751349313276095/1324537800215405753532416*b-40374630662549725282540084069465/122896428192007114981376*c+40991188782415858629190320752825/23012637096507873427456*d+13765354859219285845701862029855/3982229928972283543552*e-64806667879765933354102588502575/43949787413105820565504*f==0;
equa11sub =m-1743625504902557/524288-683191558149789503090357463411/29326767937702191104*b+22959445633915007586210679339785/202058909099976753152*c-11655028849494739207651118904051/32844485577164910592*d+652317456398320801335468445423/498874802037594112*e+383885133922523724333435256089/67259717998721024*f==0;
equa12sub =n+3878949580580463/8192+19055803659565858140764297628659/5841418173556017152*b-10006131399781328118029811914599/666592829503797504*c+20317868644705667433246067365239/498327785943072384*d-5117246172621763207417567132397/51531882592622344*e+16061175637909210839969990512723/55375433542216160*f==0;
[A, b] = equationsToMatrix([equa1sub,equa2sub,equa3sub,equa4sub,equa5sub,equa6sub,equa7sub,equa8sub,equa9sub,equa10sub,equa11sub,equa12sub],[a,b,c,d,e,f,g,h,k,l,m,n]);
sol=A\b

[Walter Roberson]

Torsten,

4154756651791824122955846205623/10141204801825835211973625643008 is approximately 1.6 * 2^101 / 2^103 . Is Octave really able to retain full https://en.wikipedia.org/wiki/Quadruple-precision_floating-point_format quadruple precision (113 bits of precision) by default?

[Walter Roberson]

equa1 to equa12 are expressions, not equations (they lack the == 0).

That is not a problem for the symbolic toolbox. Any time an expression appears in an equation context, the implication is "== 0".

[dcydhb dcydhb]

yes,and thanks you all a lot,and i think maybe the best way is to assign the values and use the

help equationsToMatrix

and it will give the precise solution,and thanks a lot again!

[dcydhb dcydhb]

and can i accept both the answers ,i think both are great helpful！

[madhan ravi]

It’s rarely possible you should press accept at both answers at the same time without minute delay both answers will be accepted I suppose. Though cannot garranty.

[Torsten]

@Walter,

I must admit that I've just checked that the code was technically correct - I didn't wait for an answer.

[dcydhb dcydhb]

when increase the Number of items of the equation and don't assign the values and i get the solution use

help equationsToMatrix

then i assign the values and get the solution,when i get the solution back in the equation,

it didn't satisify the equation and why?

codes are as this

clc;
clear all;
close all;




syms alpha0 alpha1 alpha2  alpha3 alpha4 alpha5 alpha6  alpha7  alpha8 alpha9 a0 a1 a2  a3 a4 a5 a6 a7 a8 a9;

m0=0.9112686455881505;
m1=2.920054159356038;
m2=6.17711129354441;
m3=9.354585747267652;
m4=12.513861242221347;
m5=15.666005310357953;
m6=18.814613301560172;
m7=21.961209282947657;
m8=25.106550884936922;
m9=28.251057557099365;

%即此处先不要赋值r

h=2;%水深
D1=0.8060;%圆柱吃水深度

a=2.2497;%圆柱半径

%d=h-D1;%圆柱底部到水底的距离

d=1.1940;




s0 =0.;

s1 =3.7655;

s2 =15.818;
 
s3 =36.134;

s4 =64.716;

s5 =101.56;
 
s6 =146.68;

s7 =200.06;
 
s8 =261.70;
 
s9 =331.62;





equa1 =alpha0 + (2*(a^2/4 - d^2/6))/d - (2*a1*sin(d*m1)*besselk(0, a*m1))/(d*m1*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*a2*sin(d*m2)*besselk(0, a*m2))/(d*m2*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*a3*sin(d*m3)*besselk(0, a*m3))/(d*m3*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*a4*sin(d*m4)*besselk(0, a*m4))/(d*m4*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*a5*sin(d*m5)*besselk(0, a*m5))/(d*m5*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*a6*sin(d*m6)*besselk(0, a*m6))/(d*m6*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*a7*sin(d*m7)*besselk(0, a*m7))/(d*m7*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*a8*sin(d*m8)*besselk(0, a*m8))/(d*m8*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*a9*sin(d*m9)*besselk(0, a*m9))/(d*m9*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*a0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/(d*m0*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));
 
 
equa2 =alpha1 + (2*d)/pi^2 - (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((sin(2*m1)/(4*m1) + 1/2)^(1/2)*(- d^2*m1^2 + pi^2)) - (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((sin(2*m2)/(4*m2) + 1/2)^(1/2)*(- d^2*m2^2 + pi^2)) - (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((sin(2*m3)/(4*m3) + 1/2)^(1/2)*(- d^2*m3^2 + pi^2)) - (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((sin(2*m4)/(4*m4) + 1/2)^(1/2)*(- d^2*m4^2 + pi^2)) - (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((sin(2*m5)/(4*m5) + 1/2)^(1/2)*(- d^2*m5^2 + pi^2)) - (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((sin(2*m6)/(4*m6) + 1/2)^(1/2)*(- d^2*m6^2 + pi^2)) - (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((sin(2*m7)/(4*m7) + 1/2)^(1/2)*(- d^2*m7^2 + pi^2)) - (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((sin(2*m8)/(4*m8) + 1/2)^(1/2)*(- d^2*m8^2 + pi^2)) - (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((sin(2*m9)/(4*m9) + 1/2)^(1/2)*(- d^2*m9^2 + pi^2)) + (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((sinh(2*m0)/(4*m0) + 1/2)^(1/2)*(d^2*m0^2 + pi^2));
 
 
equa3 =alpha2 - d/(2*pi^2) + (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 4*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 4*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 4*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 4*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 4*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 4*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 4*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 4*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 4*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 4*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));
 
 
equa4 =alpha3 + (2*d)/(9*pi^2) - (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 9*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 9*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 9*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 9*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 9*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 9*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 9*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 9*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 9*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 9*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));
 
 
equa5 =alpha4 - d/(8*pi^2) + (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 16*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 16*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 16*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 16*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 16*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 16*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 16*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 16*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 16*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 16*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));
 
 
equa6 =alpha5 + (2*d)/(25*pi^2) - (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 25*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 25*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 25*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 25*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 25*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 25*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 25*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 25*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 25*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 25*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));
 
 
equa7 =alpha6 - d/(18*pi^2) + (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 36*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 36*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 36*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 36*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 36*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 36*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 36*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 36*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 36*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 36*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));
 
 
equa8 =alpha7 + (2*d)/(49*pi^2) - (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 49*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 49*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 49*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 49*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 49*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 49*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 49*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 49*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 49*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 49*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));
 
 
equa9 =alpha8 - d/(32*pi^2) + (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 64*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 64*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 64*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 64*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 64*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 64*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 64*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 64*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 64*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 64*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));
 
 
equa10 =alpha9 + (2*d)/(81*pi^2) - (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 81*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 81*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 81*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 81*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 81*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 81*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 81*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 81*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 81*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 81*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));
 
 
equa11 =a0 - ((a*sinh(d*m0))/(2*d*m0*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) - (2*alpha0*s0*sinh(d*m0))/(d*m0*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) + (2*alpha1*d*m0*s1*sinh(d*m0))/((sinh(2*m0)/(4*m0) + 1/2)^(1/2)*(d^2*m0^2 + pi^2)) - (2*alpha2*d*m0*s2*sinh(d*m0))/((d^2*m0^2 + 4*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) + (2*alpha3*d*m0*s3*sinh(d*m0))/((d^2*m0^2 + 9*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) - (2*alpha4*d*m0*s4*sinh(d*m0))/((d^2*m0^2 + 16*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) + (2*alpha5*d*m0*s5*sinh(d*m0))/((d^2*m0^2 + 25*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) - (2*alpha6*d*m0*s6*sinh(d*m0))/((d^2*m0^2 + 36*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) + (2*alpha7*d*m0*s7*sinh(d*m0))/((d^2*m0^2 + 49*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) - (2*alpha8*d*m0*s8*sinh(d*m0))/((d^2*m0^2 + 64*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) + (2*alpha9*d*m0*s9*sinh(d*m0))/((d^2*m0^2 + 81*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)))/(m0*(m0*besselj(1, a*m0) + m0*bessely(1, a*m0)*i));
 
 
equa12 =a1 + ((2*alpha0*s0*sin(d*m1))/(d*m1*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (a*sin(d*m1))/(2*d*m1*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*alpha1*d*m1*s1*sin(d*m1))/((sin(2*m1)/(4*m1) + 1/2)^(1/2)*(- d^2*m1^2 + pi^2)) - (2*alpha2*d*m1*s2*sin(d*m1))/((- d^2*m1^2 + 4*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*alpha3*d*m1*s3*sin(d*m1))/((- d^2*m1^2 + 9*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*alpha4*d*m1*s4*sin(d*m1))/((- d^2*m1^2 + 16*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*alpha5*d*m1*s5*sin(d*m1))/((- d^2*m1^2 + 25*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*alpha6*d*m1*s6*sin(d*m1))/((- d^2*m1^2 + 36*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*alpha7*d*m1*s7*sin(d*m1))/((- d^2*m1^2 + 49*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*alpha8*d*m1*s8*sin(d*m1))/((- d^2*m1^2 + 64*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*alpha9*d*m1*s9*sin(d*m1))/((- d^2*m1^2 + 81*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)))/(m1^2*besselk(1, a*m1));
 
 
equa13 =a2 + ((2*alpha0*s0*sin(d*m2))/(d*m2*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (a*sin(d*m2))/(2*d*m2*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*alpha1*d*m2*s1*sin(d*m2))/((sin(2*m2)/(4*m2) + 1/2)^(1/2)*(- d^2*m2^2 + pi^2)) - (2*alpha2*d*m2*s2*sin(d*m2))/((- d^2*m2^2 + 4*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*alpha3*d*m2*s3*sin(d*m2))/((- d^2*m2^2 + 9*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*alpha4*d*m2*s4*sin(d*m2))/((- d^2*m2^2 + 16*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*alpha5*d*m2*s5*sin(d*m2))/((- d^2*m2^2 + 25*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*alpha6*d*m2*s6*sin(d*m2))/((- d^2*m2^2 + 36*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*alpha7*d*m2*s7*sin(d*m2))/((- d^2*m2^2 + 49*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*alpha8*d*m2*s8*sin(d*m2))/((- d^2*m2^2 + 64*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*alpha9*d*m2*s9*sin(d*m2))/((- d^2*m2^2 + 81*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)))/(m2^2*besselk(1, a*m2));
 
 
equa14 =a3 + ((2*alpha0*s0*sin(d*m3))/(d*m3*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (a*sin(d*m3))/(2*d*m3*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*alpha1*d*m3*s1*sin(d*m3))/((sin(2*m3)/(4*m3) + 1/2)^(1/2)*(- d^2*m3^2 + pi^2)) - (2*alpha2*d*m3*s2*sin(d*m3))/((- d^2*m3^2 + 4*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*alpha3*d*m3*s3*sin(d*m3))/((- d^2*m3^2 + 9*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*alpha4*d*m3*s4*sin(d*m3))/((- d^2*m3^2 + 16*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*alpha5*d*m3*s5*sin(d*m3))/((- d^2*m3^2 + 25*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*alpha6*d*m3*s6*sin(d*m3))/((- d^2*m3^2 + 36*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*alpha7*d*m3*s7*sin(d*m3))/((- d^2*m3^2 + 49*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*alpha8*d*m3*s8*sin(d*m3))/((- d^2*m3^2 + 64*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*alpha9*d*m3*s9*sin(d*m3))/((- d^2*m3^2 + 81*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)))/(m3^2*besselk(1, a*m3));
 
 
equa15 =a4 + ((2*alpha0*s0*sin(d*m4))/(d*m4*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (a*sin(d*m4))/(2*d*m4*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*alpha1*d*m4*s1*sin(d*m4))/((sin(2*m4)/(4*m4) + 1/2)^(1/2)*(- d^2*m4^2 + pi^2)) - (2*alpha2*d*m4*s2*sin(d*m4))/((- d^2*m4^2 + 4*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*alpha3*d*m4*s3*sin(d*m4))/((- d^2*m4^2 + 9*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*alpha4*d*m4*s4*sin(d*m4))/((- d^2*m4^2 + 16*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*alpha5*d*m4*s5*sin(d*m4))/((- d^2*m4^2 + 25*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*alpha6*d*m4*s6*sin(d*m4))/((- d^2*m4^2 + 36*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*alpha7*d*m4*s7*sin(d*m4))/((- d^2*m4^2 + 49*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*alpha8*d*m4*s8*sin(d*m4))/((- d^2*m4^2 + 64*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*alpha9*d*m4*s9*sin(d*m4))/((- d^2*m4^2 + 81*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)))/(m4^2*besselk(1, a*m4));
 
 
equa16 =a5 + ((2*alpha0*s0*sin(d*m5))/(d*m5*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (a*sin(d*m5))/(2*d*m5*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*alpha1*d*m5*s1*sin(d*m5))/((sin(2*m5)/(4*m5) + 1/2)^(1/2)*(- d^2*m5^2 + pi^2)) - (2*alpha2*d*m5*s2*sin(d*m5))/((- d^2*m5^2 + 4*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*alpha3*d*m5*s3*sin(d*m5))/((- d^2*m5^2 + 9*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*alpha4*d*m5*s4*sin(d*m5))/((- d^2*m5^2 + 16*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*alpha5*d*m5*s5*sin(d*m5))/((- d^2*m5^2 + 25*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*alpha6*d*m5*s6*sin(d*m5))/((- d^2*m5^2 + 36*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*alpha7*d*m5*s7*sin(d*m5))/((- d^2*m5^2 + 49*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*alpha8*d*m5*s8*sin(d*m5))/((- d^2*m5^2 + 64*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*alpha9*d*m5*s9*sin(d*m5))/((- d^2*m5^2 + 81*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)))/(m5^2*besselk(1, a*m5));
 
 
equa17 =a6 + ((2*alpha0*s0*sin(d*m6))/(d*m6*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (a*sin(d*m6))/(2*d*m6*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*alpha1*d*m6*s1*sin(d*m6))/((sin(2*m6)/(4*m6) + 1/2)^(1/2)*(- d^2*m6^2 + pi^2)) - (2*alpha2*d*m6*s2*sin(d*m6))/((- d^2*m6^2 + 4*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*alpha3*d*m6*s3*sin(d*m6))/((- d^2*m6^2 + 9*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*alpha4*d*m6*s4*sin(d*m6))/((- d^2*m6^2 + 16*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*alpha5*d*m6*s5*sin(d*m6))/((- d^2*m6^2 + 25*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*alpha6*d*m6*s6*sin(d*m6))/((- d^2*m6^2 + 36*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*alpha7*d*m6*s7*sin(d*m6))/((- d^2*m6^2 + 49*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*alpha8*d*m6*s8*sin(d*m6))/((- d^2*m6^2 + 64*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*alpha9*d*m6*s9*sin(d*m6))/((- d^2*m6^2 + 81*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)))/(m6^2*besselk(1, a*m6));
 
 
equa18 =a7 + ((2*alpha0*s0*sin(d*m7))/(d*m7*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (a*sin(d*m7))/(2*d*m7*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*alpha1*d*m7*s1*sin(d*m7))/((sin(2*m7)/(4*m7) + 1/2)^(1/2)*(- d^2*m7^2 + pi^2)) - (2*alpha2*d*m7*s2*sin(d*m7))/((- d^2*m7^2 + 4*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*alpha3*d*m7*s3*sin(d*m7))/((- d^2*m7^2 + 9*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*alpha4*d*m7*s4*sin(d*m7))/((- d^2*m7^2 + 16*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*alpha5*d*m7*s5*sin(d*m7))/((- d^2*m7^2 + 25*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*alpha6*d*m7*s6*sin(d*m7))/((- d^2*m7^2 + 36*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*alpha7*d*m7*s7*sin(d*m7))/((- d^2*m7^2 + 49*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*alpha8*d*m7*s8*sin(d*m7))/((- d^2*m7^2 + 64*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*alpha9*d*m7*s9*sin(d*m7))/((- d^2*m7^2 + 81*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)))/(m7^2*besselk(1, a*m7));
 
 
equa19 =a8 + ((2*alpha0*s0*sin(d*m8))/(d*m8*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (a*sin(d*m8))/(2*d*m8*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*alpha1*d*m8*s1*sin(d*m8))/((sin(2*m8)/(4*m8) + 1/2)^(1/2)*(- d^2*m8^2 + pi^2)) - (2*alpha2*d*m8*s2*sin(d*m8))/((- d^2*m8^2 + 4*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*alpha3*d*m8*s3*sin(d*m8))/((- d^2*m8^2 + 9*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*alpha4*d*m8*s4*sin(d*m8))/((- d^2*m8^2 + 16*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*alpha5*d*m8*s5*sin(d*m8))/((- d^2*m8^2 + 25*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*alpha6*d*m8*s6*sin(d*m8))/((- d^2*m8^2 + 36*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*alpha7*d*m8*s7*sin(d*m8))/((- d^2*m8^2 + 49*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*alpha8*d*m8*s8*sin(d*m8))/((- d^2*m8^2 + 64*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*alpha9*d*m8*s9*sin(d*m8))/((- d^2*m8^2 + 81*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)))/(m8^2*besselk(1, a*m8));
 
 
equa20 =a9 + ((2*alpha0*s0*sin(d*m9))/(d*m9*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (a*sin(d*m9))/(2*d*m9*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*alpha1*d*m9*s1*sin(d*m9))/((sin(2*m9)/(4*m9) + 1/2)^(1/2)*(- d^2*m9^2 + pi^2)) - (2*alpha2*d*m9*s2*sin(d*m9))/((- d^2*m9^2 + 4*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*alpha3*d*m9*s3*sin(d*m9))/((- d^2*m9^2 + 9*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*alpha4*d*m9*s4*sin(d*m9))/((- d^2*m9^2 + 16*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*alpha5*d*m9*s5*sin(d*m9))/((- d^2*m9^2 + 25*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*alpha6*d*m9*s6*sin(d*m9))/((- d^2*m9^2 + 36*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*alpha7*d*m9*s7*sin(d*m9))/((- d^2*m9^2 + 49*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*alpha8*d*m9*s8*sin(d*m9))/((- d^2*m9^2 + 64*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*alpha9*d*m9*s9*sin(d*m9))/((- d^2*m9^2 + 81*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)))/(m9^2*besselk(1, a*m9));
 



[A, b] = equationsToMatrix([equa1,equa2,equa3,equa4,equa5,equa6,equa7,equa8,equa9,equa10,equa11,equa12,equa13,equa14,equa15,equa16,equa17,equa18,equa19,equa20], [alpha0, alpha1,alpha2, alpha3, alpha4,alpha5,alpha6, alpha7, alpha8,alpha9,a0,a1,a2 ,a3,a4,a5,a6,a7,a8,a9]);


x = A\b;



alpha0=vpa(x(1),40)
alpha1 =vpa(x(2),40)
alpha2 =vpa(x(3),40)
alpha3=vpa(x(4),40)
alpha4 = vpa(x(5),40)
alpha5 =vpa(x(6),40)
 
alpha6=vpa(x(7),40)
alpha7 =vpa(x(8),40)
alpha8 =vpa(x(9),40)
alpha9=vpa(x(10),40)
 
 
  a0  = vpa(x(11),40)
  a1 = vpa(x(12),40)
  a2 =  vpa(x(13),40)
    a3  = vpa(x(14),40)
  a4 =  vpa(x(15),40)
  a5 = vpa(x(16),40)
  
   a6  = vpa(x(17),40)
  a7 = vpa(x(18),40)
  a8 =  vpa(x(19),40)
    a9  = vpa(x(20),40)

and when i get the solution and get it back in the 20 equations,it runs out as this

    equa1 =

  4.4409e-016 +4.4409e-016i


equa2 =

 -8.3267e-017 -8.3267e-017i


equa3 =

  1.7347e-017 +2.7756e-017i


equa4 =

            0 -3.4694e-018i


equa5 =

     0


equa6 =

  4.3368e-018 +1.7347e-018i


equa7 =

  1.3010e-018 +2.6021e-018i


equa8 =

  1.0408e-017 +6.9389e-018i


equa9 =

  2.6021e-018 +2.1684e-018i


equa10 =

  1.3661e-017 +8.2399e-018i


equa11 =

            0 -8.3267e-017i


equa12 =

  5.6843e-014 +2.8422e-014i


equa13 =

 -5.4570e-011 -2.9104e-011i


equa14 =

 -1.3737e-008 -1.4319e-008i


equa15 =

 -3.0518e-005 -9.5367e-006i


equa16 =

  -0.0391 - 0.0195i


equa17 =

 -68.0000 -40.0000i


equa18 =

 -7.3728e+004 -4.0960e+004i


equa19 =

 -2.6844e+008 -1.6777e+008i


equa20 =

 -1.2885e+010 -4.2950e+009i

>> 

[Walter Roberson]

Try this small modification:

%clc;
%clear all;
%close all;
syms alpha0 alpha1 alpha2  alpha3 alpha4 alpha5 alpha6  alpha7  alpha8 alpha9 a0 a1 a2  a3 a4 a5 a6 a7 a8 a9;
m0=0.9112686455881505;
m1=2.920054159356038;
m2=6.17711129354441;
m3=9.354585747267652;
m4=12.513861242221347;
m5=15.666005310357953;
m6=18.814613301560172;
m7=21.961209282947657;
m8=25.106550884936922;
m9=28.251057557099365;
%即此处先不要赋值r
h=2;%水深
D1=0.8060;%圆柱吃水深度
a=2.2497;%圆柱半径
%d=h-D1;%圆柱底部到水底的距离
d=1.1940;
s0 =0.;
s1 =3.7655;
s2 =15.818;

s3 =36.134;
s4 =64.716;
s5 =101.56;

s6 =146.68;
s7 =200.06;

s8 =261.70;

s9 =331.62;
equa1 =alpha0 + (2*(a^2/4 - d^2/6))/d - (2*a1*sin(d*m1)*besselk(0, a*m1))/(d*m1*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*a2*sin(d*m2)*besselk(0, a*m2))/(d*m2*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*a3*sin(d*m3)*besselk(0, a*m3))/(d*m3*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*a4*sin(d*m4)*besselk(0, a*m4))/(d*m4*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*a5*sin(d*m5)*besselk(0, a*m5))/(d*m5*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*a6*sin(d*m6)*besselk(0, a*m6))/(d*m6*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*a7*sin(d*m7)*besselk(0, a*m7))/(d*m7*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*a8*sin(d*m8)*besselk(0, a*m8))/(d*m8*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*a9*sin(d*m9)*besselk(0, a*m9))/(d*m9*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*a0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/(d*m0*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));


equa2 =alpha1 + (2*d)/pi^2 - (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((sin(2*m1)/(4*m1) + 1/2)^(1/2)*(- d^2*m1^2 + pi^2)) - (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((sin(2*m2)/(4*m2) + 1/2)^(1/2)*(- d^2*m2^2 + pi^2)) - (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((sin(2*m3)/(4*m3) + 1/2)^(1/2)*(- d^2*m3^2 + pi^2)) - (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((sin(2*m4)/(4*m4) + 1/2)^(1/2)*(- d^2*m4^2 + pi^2)) - (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((sin(2*m5)/(4*m5) + 1/2)^(1/2)*(- d^2*m5^2 + pi^2)) - (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((sin(2*m6)/(4*m6) + 1/2)^(1/2)*(- d^2*m6^2 + pi^2)) - (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((sin(2*m7)/(4*m7) + 1/2)^(1/2)*(- d^2*m7^2 + pi^2)) - (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((sin(2*m8)/(4*m8) + 1/2)^(1/2)*(- d^2*m8^2 + pi^2)) - (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((sin(2*m9)/(4*m9) + 1/2)^(1/2)*(- d^2*m9^2 + pi^2)) + (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((sinh(2*m0)/(4*m0) + 1/2)^(1/2)*(d^2*m0^2 + pi^2));


equa3 =alpha2 - d/(2*pi^2) + (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 4*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 4*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 4*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 4*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 4*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 4*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 4*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 4*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 4*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 4*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));


equa4 =alpha3 + (2*d)/(9*pi^2) - (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 9*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 9*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 9*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 9*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 9*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 9*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 9*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 9*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 9*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 9*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));


equa5 =alpha4 - d/(8*pi^2) + (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 16*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 16*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 16*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 16*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 16*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 16*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 16*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 16*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 16*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 16*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));


equa6 =alpha5 + (2*d)/(25*pi^2) - (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 25*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 25*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 25*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 25*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 25*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 25*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 25*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 25*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 25*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 25*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));


equa7 =alpha6 - d/(18*pi^2) + (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 36*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 36*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 36*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 36*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 36*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 36*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 36*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 36*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 36*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 36*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));


equa8 =alpha7 + (2*d)/(49*pi^2) - (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 49*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 49*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 49*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 49*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 49*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 49*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 49*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 49*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 49*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 49*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));


equa9 =alpha8 - d/(32*pi^2) + (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 64*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 64*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 64*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 64*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 64*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 64*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 64*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 64*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 64*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 64*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));


equa10 =alpha9 + (2*d)/(81*pi^2) - (2*a1*d*m1*sin(d*m1)*besselk(0, a*m1))/((- d^2*m1^2 + 81*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*a2*d*m2*sin(d*m2)*besselk(0, a*m2))/((- d^2*m2^2 + 81*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*a3*d*m3*sin(d*m3)*besselk(0, a*m3))/((- d^2*m3^2 + 81*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*a4*d*m4*sin(d*m4)*besselk(0, a*m4))/((- d^2*m4^2 + 81*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*a5*d*m5*sin(d*m5)*besselk(0, a*m5))/((- d^2*m5^2 + 81*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*a6*d*m6*sin(d*m6)*besselk(0, a*m6))/((- d^2*m6^2 + 81*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*a7*d*m7*sin(d*m7)*besselk(0, a*m7))/((- d^2*m7^2 + 81*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*a8*d*m8*sin(d*m8)*besselk(0, a*m8))/((- d^2*m8^2 + 81*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*a9*d*m9*sin(d*m9)*besselk(0, a*m9))/((- d^2*m9^2 + 81*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*a0*d*m0*sinh(d*m0)*(besselj(0, a*m0) + bessely(0, a*m0)*i))/((d^2*m0^2 + 81*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2));


equa11 =a0 - ((a*sinh(d*m0))/(2*d*m0*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) - (2*alpha0*s0*sinh(d*m0))/(d*m0*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) + (2*alpha1*d*m0*s1*sinh(d*m0))/((sinh(2*m0)/(4*m0) + 1/2)^(1/2)*(d^2*m0^2 + pi^2)) - (2*alpha2*d*m0*s2*sinh(d*m0))/((d^2*m0^2 + 4*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) + (2*alpha3*d*m0*s3*sinh(d*m0))/((d^2*m0^2 + 9*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) - (2*alpha4*d*m0*s4*sinh(d*m0))/((d^2*m0^2 + 16*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) + (2*alpha5*d*m0*s5*sinh(d*m0))/((d^2*m0^2 + 25*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) - (2*alpha6*d*m0*s6*sinh(d*m0))/((d^2*m0^2 + 36*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) + (2*alpha7*d*m0*s7*sinh(d*m0))/((d^2*m0^2 + 49*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) - (2*alpha8*d*m0*s8*sinh(d*m0))/((d^2*m0^2 + 64*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)) + (2*alpha9*d*m0*s9*sinh(d*m0))/((d^2*m0^2 + 81*pi^2)*(sinh(2*m0)/(4*m0) + 1/2)^(1/2)))/(m0*(m0*besselj(1, a*m0) + m0*bessely(1, a*m0)*i));


equa12 =a1 + ((2*alpha0*s0*sin(d*m1))/(d*m1*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (a*sin(d*m1))/(2*d*m1*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*alpha1*d*m1*s1*sin(d*m1))/((sin(2*m1)/(4*m1) + 1/2)^(1/2)*(- d^2*m1^2 + pi^2)) - (2*alpha2*d*m1*s2*sin(d*m1))/((- d^2*m1^2 + 4*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*alpha3*d*m1*s3*sin(d*m1))/((- d^2*m1^2 + 9*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*alpha4*d*m1*s4*sin(d*m1))/((- d^2*m1^2 + 16*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*alpha5*d*m1*s5*sin(d*m1))/((- d^2*m1^2 + 25*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*alpha6*d*m1*s6*sin(d*m1))/((- d^2*m1^2 + 36*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*alpha7*d*m1*s7*sin(d*m1))/((- d^2*m1^2 + 49*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) - (2*alpha8*d*m1*s8*sin(d*m1))/((- d^2*m1^2 + 64*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)) + (2*alpha9*d*m1*s9*sin(d*m1))/((- d^2*m1^2 + 81*pi^2)*(sin(2*m1)/(4*m1) + 1/2)^(1/2)))/(m1^2*besselk(1, a*m1));


equa13 =a2 + ((2*alpha0*s0*sin(d*m2))/(d*m2*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (a*sin(d*m2))/(2*d*m2*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*alpha1*d*m2*s1*sin(d*m2))/((sin(2*m2)/(4*m2) + 1/2)^(1/2)*(- d^2*m2^2 + pi^2)) - (2*alpha2*d*m2*s2*sin(d*m2))/((- d^2*m2^2 + 4*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*alpha3*d*m2*s3*sin(d*m2))/((- d^2*m2^2 + 9*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*alpha4*d*m2*s4*sin(d*m2))/((- d^2*m2^2 + 16*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*alpha5*d*m2*s5*sin(d*m2))/((- d^2*m2^2 + 25*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*alpha6*d*m2*s6*sin(d*m2))/((- d^2*m2^2 + 36*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*alpha7*d*m2*s7*sin(d*m2))/((- d^2*m2^2 + 49*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) - (2*alpha8*d*m2*s8*sin(d*m2))/((- d^2*m2^2 + 64*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)) + (2*alpha9*d*m2*s9*sin(d*m2))/((- d^2*m2^2 + 81*pi^2)*(sin(2*m2)/(4*m2) + 1/2)^(1/2)))/(m2^2*besselk(1, a*m2));


equa14 =a3 + ((2*alpha0*s0*sin(d*m3))/(d*m3*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (a*sin(d*m3))/(2*d*m3*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*alpha1*d*m3*s1*sin(d*m3))/((sin(2*m3)/(4*m3) + 1/2)^(1/2)*(- d^2*m3^2 + pi^2)) - (2*alpha2*d*m3*s2*sin(d*m3))/((- d^2*m3^2 + 4*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*alpha3*d*m3*s3*sin(d*m3))/((- d^2*m3^2 + 9*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*alpha4*d*m3*s4*sin(d*m3))/((- d^2*m3^2 + 16*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*alpha5*d*m3*s5*sin(d*m3))/((- d^2*m3^2 + 25*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*alpha6*d*m3*s6*sin(d*m3))/((- d^2*m3^2 + 36*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*alpha7*d*m3*s7*sin(d*m3))/((- d^2*m3^2 + 49*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) - (2*alpha8*d*m3*s8*sin(d*m3))/((- d^2*m3^2 + 64*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)) + (2*alpha9*d*m3*s9*sin(d*m3))/((- d^2*m3^2 + 81*pi^2)*(sin(2*m3)/(4*m3) + 1/2)^(1/2)))/(m3^2*besselk(1, a*m3));


equa15 =a4 + ((2*alpha0*s0*sin(d*m4))/(d*m4*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (a*sin(d*m4))/(2*d*m4*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*alpha1*d*m4*s1*sin(d*m4))/((sin(2*m4)/(4*m4) + 1/2)^(1/2)*(- d^2*m4^2 + pi^2)) - (2*alpha2*d*m4*s2*sin(d*m4))/((- d^2*m4^2 + 4*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*alpha3*d*m4*s3*sin(d*m4))/((- d^2*m4^2 + 9*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*alpha4*d*m4*s4*sin(d*m4))/((- d^2*m4^2 + 16*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*alpha5*d*m4*s5*sin(d*m4))/((- d^2*m4^2 + 25*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*alpha6*d*m4*s6*sin(d*m4))/((- d^2*m4^2 + 36*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*alpha7*d*m4*s7*sin(d*m4))/((- d^2*m4^2 + 49*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) - (2*alpha8*d*m4*s8*sin(d*m4))/((- d^2*m4^2 + 64*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)) + (2*alpha9*d*m4*s9*sin(d*m4))/((- d^2*m4^2 + 81*pi^2)*(sin(2*m4)/(4*m4) + 1/2)^(1/2)))/(m4^2*besselk(1, a*m4));


equa16 =a5 + ((2*alpha0*s0*sin(d*m5))/(d*m5*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (a*sin(d*m5))/(2*d*m5*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*alpha1*d*m5*s1*sin(d*m5))/((sin(2*m5)/(4*m5) + 1/2)^(1/2)*(- d^2*m5^2 + pi^2)) - (2*alpha2*d*m5*s2*sin(d*m5))/((- d^2*m5^2 + 4*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*alpha3*d*m5*s3*sin(d*m5))/((- d^2*m5^2 + 9*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*alpha4*d*m5*s4*sin(d*m5))/((- d^2*m5^2 + 16*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*alpha5*d*m5*s5*sin(d*m5))/((- d^2*m5^2 + 25*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*alpha6*d*m5*s6*sin(d*m5))/((- d^2*m5^2 + 36*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*alpha7*d*m5*s7*sin(d*m5))/((- d^2*m5^2 + 49*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) - (2*alpha8*d*m5*s8*sin(d*m5))/((- d^2*m5^2 + 64*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)) + (2*alpha9*d*m5*s9*sin(d*m5))/((- d^2*m5^2 + 81*pi^2)*(sin(2*m5)/(4*m5) + 1/2)^(1/2)))/(m5^2*besselk(1, a*m5));


equa17 =a6 + ((2*alpha0*s0*sin(d*m6))/(d*m6*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (a*sin(d*m6))/(2*d*m6*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*alpha1*d*m6*s1*sin(d*m6))/((sin(2*m6)/(4*m6) + 1/2)^(1/2)*(- d^2*m6^2 + pi^2)) - (2*alpha2*d*m6*s2*sin(d*m6))/((- d^2*m6^2 + 4*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*alpha3*d*m6*s3*sin(d*m6))/((- d^2*m6^2 + 9*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*alpha4*d*m6*s4*sin(d*m6))/((- d^2*m6^2 + 16*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*alpha5*d*m6*s5*sin(d*m6))/((- d^2*m6^2 + 25*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*alpha6*d*m6*s6*sin(d*m6))/((- d^2*m6^2 + 36*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*alpha7*d*m6*s7*sin(d*m6))/((- d^2*m6^2 + 49*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) - (2*alpha8*d*m6*s8*sin(d*m6))/((- d^2*m6^2 + 64*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)) + (2*alpha9*d*m6*s9*sin(d*m6))/((- d^2*m6^2 + 81*pi^2)*(sin(2*m6)/(4*m6) + 1/2)^(1/2)))/(m6^2*besselk(1, a*m6));


equa18 =a7 + ((2*alpha0*s0*sin(d*m7))/(d*m7*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (a*sin(d*m7))/(2*d*m7*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*alpha1*d*m7*s1*sin(d*m7))/((sin(2*m7)/(4*m7) + 1/2)^(1/2)*(- d^2*m7^2 + pi^2)) - (2*alpha2*d*m7*s2*sin(d*m7))/((- d^2*m7^2 + 4*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*alpha3*d*m7*s3*sin(d*m7))/((- d^2*m7^2 + 9*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*alpha4*d*m7*s4*sin(d*m7))/((- d^2*m7^2 + 16*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*alpha5*d*m7*s5*sin(d*m7))/((- d^2*m7^2 + 25*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*alpha6*d*m7*s6*sin(d*m7))/((- d^2*m7^2 + 36*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*alpha7*d*m7*s7*sin(d*m7))/((- d^2*m7^2 + 49*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) - (2*alpha8*d*m7*s8*sin(d*m7))/((- d^2*m7^2 + 64*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)) + (2*alpha9*d*m7*s9*sin(d*m7))/((- d^2*m7^2 + 81*pi^2)*(sin(2*m7)/(4*m7) + 1/2)^(1/2)))/(m7^2*besselk(1, a*m7));


equa19 =a8 + ((2*alpha0*s0*sin(d*m8))/(d*m8*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (a*sin(d*m8))/(2*d*m8*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*alpha1*d*m8*s1*sin(d*m8))/((sin(2*m8)/(4*m8) + 1/2)^(1/2)*(- d^2*m8^2 + pi^2)) - (2*alpha2*d*m8*s2*sin(d*m8))/((- d^2*m8^2 + 4*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*alpha3*d*m8*s3*sin(d*m8))/((- d^2*m8^2 + 9*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*alpha4*d*m8*s4*sin(d*m8))/((- d^2*m8^2 + 16*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*alpha5*d*m8*s5*sin(d*m8))/((- d^2*m8^2 + 25*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*alpha6*d*m8*s6*sin(d*m8))/((- d^2*m8^2 + 36*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*alpha7*d*m8*s7*sin(d*m8))/((- d^2*m8^2 + 49*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) - (2*alpha8*d*m8*s8*sin(d*m8))/((- d^2*m8^2 + 64*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)) + (2*alpha9*d*m8*s9*sin(d*m8))/((- d^2*m8^2 + 81*pi^2)*(sin(2*m8)/(4*m8) + 1/2)^(1/2)))/(m8^2*besselk(1, a*m8));


equa20 =a9 + ((2*alpha0*s0*sin(d*m9))/(d*m9*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (a*sin(d*m9))/(2*d*m9*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*alpha1*d*m9*s1*sin(d*m9))/((sin(2*m9)/(4*m9) + 1/2)^(1/2)*(- d^2*m9^2 + pi^2)) - (2*alpha2*d*m9*s2*sin(d*m9))/((- d^2*m9^2 + 4*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*alpha3*d*m9*s3*sin(d*m9))/((- d^2*m9^2 + 9*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*alpha4*d*m9*s4*sin(d*m9))/((- d^2*m9^2 + 16*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*alpha5*d*m9*s5*sin(d*m9))/((- d^2*m9^2 + 25*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*alpha6*d*m9*s6*sin(d*m9))/((- d^2*m9^2 + 36*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*alpha7*d*m9*s7*sin(d*m9))/((- d^2*m9^2 + 49*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) - (2*alpha8*d*m9*s8*sin(d*m9))/((- d^2*m9^2 + 64*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)) + (2*alpha9*d*m9*s9*sin(d*m9))/((- d^2*m9^2 + 81*pi^2)*(sin(2*m9)/(4*m9) + 1/2)^(1/2)))/(m9^2*besselk(1, a*m9));

equ = [equa1,equa2,equa3,equa4,equa5,equa6,equa7,equa8,equa9,equa10,equa11,equa12,equa13,equa14,equa15,equa16,equa17,equa18,equa19,equa20];
vars = [alpha0, alpha1,alpha2, alpha3, alpha4,alpha5,alpha6, alpha7, alpha8,alpha9,a0,a1,a2 ,a3,a4,a5,a6,a7,a8,a9];
[A, b] = equationsToMatrix(equ, vars);
x = A\b;
alpha0=vpa(x(1),40)
alpha1 =vpa(x(2),40)
alpha2 =vpa(x(3),40)
alpha3=vpa(x(4),40)
alpha4 = vpa(x(5),40)
alpha5 =vpa(x(6),40)

alpha6=vpa(x(7),40)
alpha7 =vpa(x(8),40)
alpha8 =vpa(x(9),40)
alpha9=vpa(x(10),40)


a0  = vpa(x(11),40)
a1 = vpa(x(12),40)
a2 =  vpa(x(13),40)
a3  = vpa(x(14),40)
a4 =  vpa(x(15),40)
a5 = vpa(x(16),40)

a6  = vpa(x(17),40)
a7 = vpa(x(18),40)
a8 =  vpa(x(19),40)
a9  = vpa(x(20),40)

subs(equ, vars, x.')
subs(equ, vars, vpa(x.', 40))
subs(equ, vars, [alpha0, alpha1,alpha2, alpha3, alpha4,alpha5,alpha6, alpha7, alpha8,alpha9,a0,a1,a2 ,a3,a4,a5,a6,a7,a8,a9])

The output I get with modern MATLAB is

ans =

[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

ans =

[ 1.8367099231598242312011508394098e-40, -1.1479437019748901445007192746311e-41, -5.7397185098744507225035963731555e-42, 5.7397185098744507225035963731555e-42i, 0, - 7.1746481373430634031294954664444e-43 - 2.8698592549372253612517981865777e-42i, 1.7936620343357658507823738666111e-42, 7.1746481373430634031294954664444e-43 + 3.5873240686715317015647477332222e-43i, 7.1746481373430634031294954664444e-43, 0, 9.1835496157991211560057541970488e-41i, 5.8774717541114375398436826861112e-39 + 5.3264587771634902704833374342883e-39i, - 1.2037062152420224081599862141156e-35 + 9.0277966143151680611998966058668e-36i, - 3.0814879110195773648895647081359e-33 - 0.000000000000000000000000000000013866695599588098142003041186611i, 0.0000000000000000000000000000031554436208840472216469142611311, 0.0000000000000000000000000060584517520973706655620753813718 - 0.0000000000000000000000000022214323091023692440394276398363i, - 0.0000000000000000000000099261673506363320984569043048396 + 0.0000000000000000000000016543612251060553497428173841399i, 0.0000000000000000000016940658945086006781366450013593 + 0.0000000000000000000033881317890172013562732900027186i, 0.0000000000000000069388939039072283776476979255676, -0.0000000000000035527136788005009293556213378906i]

ans =

[ 1.8367099231598242312011508394098e-40, -1.1479437019748901445007192746311e-41, -5.7397185098744507225035963731555e-42, 5.7397185098744507225035963731555e-42i, 0, - 7.1746481373430634031294954664444e-43 - 2.8698592549372253612517981865777e-42i, 1.7936620343357658507823738666111e-42, 7.1746481373430634031294954664444e-43 + 3.5873240686715317015647477332222e-43i, 7.1746481373430634031294954664444e-43, 0, 9.1835496157991211560057541970488e-41i, 5.8774717541114375398436826861112e-39 + 5.3264587771634902704833374342883e-39i, - 1.2037062152420224081599862141156e-35 + 9.0277966143151680611998966058668e-36i, - 3.0814879110195773648895647081359e-33 - 0.000000000000000000000000000000013866695599588098142003041186611i, 0.0000000000000000000000000000031554436208840472216469142611311, 0.0000000000000000000000000060584517520973706655620753813718 - 0.0000000000000000000000000022214323091023692440394276398363i, - 0.0000000000000000000000099261673506363320984569043048396 + 0.0000000000000000000000016543612251060553497428173841399i, 0.0000000000000000000016940658945086006781366450013593 + 0.0000000000000000000033881317890172013562732900027186i, 0.0000000000000000069388939039072283776476979255676, -0.0000000000000035527136788005009293556213378906i]

and

>> ans(17)

ans =

- 0.0000000000000000000000099261673506363320984569043048396 + 0.0000000000000000000000016543612251060553497428173841399i

That value corresponds to what you show as

equa17 =

-68.0000 -40.0000i

If you still see a -68 in that position then it is probably because you are using an rather old MATLAB. If you see a value on the same scale of what I post here then you are doing something wrong in doing the back-substitutions.

[dcydhb dcydhb]

surely your mathod has a good result,and i have get you solution in the my equation,and in matlab 7 it runs out as this

equa1 =

  4.4409e-016 +4.4409e-016i


equa2 =

 -8.3267e-017 -8.3267e-017i


equa3 =

  1.7347e-017 +2.7756e-017i


equa4 =

            0 -3.4694e-018i


equa5 =

     0


equa6 =

  4.3368e-018 +1.7347e-018i


equa7 =

  1.3010e-018 +2.6021e-018i


equa8 =

  1.0408e-017 +6.9389e-018i


equa9 =

  2.6021e-018 +2.1684e-018i


equa10 =

  1.3661e-017 +8.2399e-018i


equa11 =

            0 -8.3267e-017i


equa12 =

  5.6843e-014 +2.8422e-014i


equa13 =

 -5.4570e-011 -2.9104e-011i


equa14 =

 -1.3737e-008 -1.4319e-008i


equa15 =

 -3.0518e-005 -9.5367e-006i


equa16 =

  -0.0391 - 0.0195i


equa17 =

 -68.0000 -40.0000i


equa18 =

 -7.3728e+004 -4.0960e+004i


equa19 =

 -2.6844e+008 -1.6777e+008i


equa20 =

 -1.2885e+010 -4.2950e+009i

>> 

it means the original solution is right but the way to get in the equation is different,

and i get the solution in the my equation in r2014a, it runs out as this

equa1 =

  -2.2204e-16 + 2.2204e-16i


equa2 =

  -1.3878e-17 + 5.5511e-17i


equa3 =

   0.0000e+00 - 6.9389e-18i


equa4 =

  -6.9389e-18 + 3.4694e-18i


equa5 =

   0.0000e+00 - 1.7347e-18i


equa6 =

  -1.7347e-18


equa7 =

  -8.6736e-19


equa8 =

   0.0000e+00 + 1.7347e-18i


equa9 =

   0.0000e+00 - 8.6736e-19i


equa10 =

   4.3368e-19 + 4.3368e-19i


equa11 =

   0.0000e+00 + 2.7756e-17i


equa12 =

   2.8422e-14 + 1.4211e-14i


equa13 =

  -2.1828e-11 - 3.6380e-12i


equa14 =

  -1.5367e-08 - 1.3504e-08i


equa15 =

  -1.1444e-05 + 3.8147e-06i


equa16 =

  -0.0039 + 0.0039i


equa17 =

   0.0000 + 4.0000i


equa18 =

   0.0000e+00 + 4.0960e+03i


equa19 =

     0


equa20 =

  -4.2950e+09 + 2.1475e+09i

>> 

only the equa20 is abnormal,and why in your method they are all zero?

[Walter Roberson]

There is something wrong with the way you are constructing the numeric equa* values. I tested in MATLAB R2014a and do not get the same values you get. After the last subs() in the code I posted,

double(max(abs(ans)))

gives 3.9721e-15

I do get slightly different values between R2014a and current MATLAB, but max(abs()) of the difference between the two is less than 4E-15 (indeed, it is almost exactly the same as that 3.9721e-15 figure.)

[dcydhb dcydhb]

double(max(abs(ans)))

what do it mean？

i posted it as

subs(equ, vars, x.')
subs(equ, vars, vpa(x.', 20))
subs(equ, vars, [alpha0, alpha1,alpha2, alpha3, alpha4,alpha5,alpha6, alpha7, alpha8,alpha9,a0,a1,a2 ,a3,a4,a5,a6,a7,a8,a9])

double(max(abs(ans)))

and got

ans =

   6.6564e-04

i just want to konw why directly get it in the equation makes a great difference?

[Walter Roberson]

The last subs() effectively constructs the equa* values in vectorized form -- the first element of the output is equa1, the second is equa2, and so on.

ans after that third calculation is the vector [equa1, equa2, ....] . abs() of that gives the absolute magnitude, the distance from the entries to 0. max() gets the largest of the absolute magnitudes, and double() converts from symbolic to floating point. So double(max(abs(ans))) is calculated the upper bound on how "bad" the solutions are. You are now getting about 6.6E-4, but what you posted earlier where equa20 = -4.2950e+09 + 2.1475e+09i would have given a max absolute value at least 4.8E+9 .

So there is something wrong with the way you calculate your equa* values. The actual error limit of the calculation is much much smaller than what you are seeing with the equa* that you are calculating somehow. Your equa* values should be almost exactly the same as the result of that subs(equ, vars, vpa(x.', 20)) calculation.