no explicit solution for solve
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I tried to solve a system of non-linear equations and it came back with the comment,"Explicit solution could not be found." Here is the part of codes with involved the equations. Anything undefined in the syms were considered as the constants:
value=50;
syms x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 positive
solve(...
x10==value,...
x11==N*x8^4/(x8^4+Kb*x9^4),...
x1*(lamQs+muD)==(kPqloop*x11+kPqunloop*(N-x11))*(Kq*x5)/(1+Kq*x5),...
x2*(lamQl+muD)==(kPqloop*x11+kPqunloop*(N-x11))/(1+Kq*x5),...
x3*(lamQar+muD+kar*x5+kar*x4)==kPqloop*x11+kPqunloop*(N-x11),...
x4*(lamX+muD+kar*x3)==kxloop*x11+kxunloop*(N-x11),...
x5*(lamXar+muD+kar*x3)==kXarloop*x11+kXarunloop*(N-x11)-(kPqloop*x11+kPqunloop*(N-x11))*(Kq*x5)/(1+Kq*x5),...
x6*lameI==ki*(x1+x2)*DDensity-kTi*(x6-x8)*DDensity,...
x8*(lamiI+muD)==kTi*(x6-x8),...
x9*(lamiC+muD)==kTc*(x7-x9),...
x10*(lamPrgB+muD)==kdown*x2,...
x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11);
and here are the constants:
N=5/0.602;
muD=log(2)/(45*60);
%muR=3.35*10^-4;
kPqloop=7.23*10^-3;
kPqunloop=8.871*10^-2;
kXarloop=1.021*10^-2;
kXarunloop=1.21*10^-3;
kxloop=8.23*10^-3;
kxunloop=1.21*10^-3;
kQarloop=1.8*10^-3;
kQarunloop=1.08*10^-2;
kconj=2*10^-4;
ki=10^-2;
p=10^-11;
kTi=10^-4;
kTc=10^-3;
%kc=1.2*10^-1;
kar=10^-3;
Kq=4.43;
Kb=10^6;
kdown=10^-3;
lamQs=10^-4;
lamQl=0.1;
lamXar=3.851*10^-4;
lamQar=10^-3;
lamX=10^-4;
lameI=10^-6;
lameC=10^-6;
lamiI=10^-6;
lamiC=10^-6;
lamPrgB=10^-3;
DDensity=5*10^7;
Thanks
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John D'Errico
2014년 7월 31일
So? That is the problem with ANY root finding problem. Only global methods can try to find all solutions, and even they can only try. Given a nasty enough problem, any root finder can have problems finding them all.
Accept that you will never be able to find all solutions using exact methods. Wanting to do the impossible is a nice goal, but still impossible.
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