How to calculation this integral ?

조회 수: 1 (최근 30일)
Arash Shahpasand
Arash Shahpasand 2021년 1월 30일
댓글: Walter Roberson 2021년 3월 3일
L0 = 0:20
M0 = -20:20
N0 = 0:20
C = 10 ,
b = 0 ,
V = 2/3 ,
V1 = 2.0001/3 ,
K = 2*pi ,
"EpsilonN : E(n=0) = 1 and for E(n>=1)=2 ",
EpsilonN = [1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2]
%-------------------------------------------------------------------------------------------------------
for L1 = 0:length(L0)
for M1 = 0:length(M0)
for N1 = 0:length(N0)
if (L1/V1)+M1 ~= (N1/V0) %SA1 ~= abs(SA2)
Clmn = (EpsilonN/2*V0*pi)*besselj(M1,K*B)*((sin(((L1/V1)+M1+(N1/V0))*V0*pi)/(L1/V1)+M1+(N1/V0))+...
(sin(((L1/V1)+M1-(N1/V0))*V0*pi)/(L1/V1)+M1-(N1/V0))); %<part 1>
else N1 ~= 0 %n ~= 0 ,
Clmn = (EpsilonN/2)*besselj(M1,K*B) ; %<part 3>
if (L1/V1)+M1 == (N1/V0) %SA1 == SA2 ,
Clmn = EpsilonN*besselj(M1,K*B); %<part 2>
end
end
end
end
end
Clmn

이 질문에 답변하려면 로그인하십시오.

답변 (1개)

Walter Roberson
Walter Roberson 2021년 2월 3일
Ran in:
format long g
L0 = 0:20;
M0 = -20:20;
N0 = 0:20;
C = 10;
b = 0;
V = 2/3;
V1 = 2.0001/3;
K = 2*pi;
%"EpsilonN : E(n=0) = 1 and for E(n>=1)=2 ",
EpsilonN = 2 * ones(size(N0));
EpsilonN(N0 == 0) = 1;
%-------------------------------------------------------------------------------------------------------
for L1 = 1:length(L0)
L = L0(L1);
for M1 = 1:length(M0)
M = M0(M1);
for N1 = 1:length(N0)
N = N0(N1);
EpsN = EpsilonN(N1);
if abs((L/V1)+M) ~= abs(N/V)
C = (EpsN/2*V*pi)*besselj(M,K*b)*((sin(((L/V1)+M+(N/V))*V*pi)/(L/V1)+M+(N/V))+...
(sin(((L/V1)+M-(N/V))*V*pi)/(L/V1)+M-(N/V))); %<part 1>
elseif N ~= 0
C = (EpsN/2)*besselj(M,K*b) ; %<part 3>
else
C = EpsN*besselj(M,K*b); %<part 2>
end
Clmn(L1, M1, N1) = C;
end
end
end
Clmn
Clmn =
Clmn(:,:,1) = NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN 1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000219324541345203 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000219324538639666 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000219324534130437 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000219324527817516 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000219324519700904 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.0002193245097806 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000219324498056251 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.00021932448452892 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000219324469197819 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000219324452062476 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000219324433124846 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000219324412381271 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000219324389834943 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000219324365484953 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000219324339331957 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000219324311374587 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000219324281613548 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000219324250049389 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000219324216680976 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000219324181508891 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Clmn(:,:,2) = NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438649082691512 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0004386490772802 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438649068260572 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438649055634953 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438649039401948 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438649019561557 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.00043864899611285 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438648969058151 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438648938395602 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438648904126131 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438648866249274 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438648824761776 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438648779670612 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438648730970667 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438648678662871 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438648622750013 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438648563227445 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438648500098885 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438648433362474 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438648363017747 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Clmn(:,:,3) = NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN 0 NaN NaN NaN NaN NaN 0 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438649082690117 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438649077279735 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438649068261502 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438649055636348 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438649039402413 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438649019561557 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438648996111919 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438648969057221 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438648938394672 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438648904125201 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438648866249739 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.000438648824761776 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.000438648779670612 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  댓글 수: 3
이전 댓글 1개 표시
Walter Roberson
Walter Roberson 2021년 2월 5일
Do not use symsum() for that purpose. Calculate an array of besselj((l/V1)+m,K*C) values that is length(L0) by length(M0), and use .* against Clmn, and sum() that across the second dimension. Construct a vector of B values that is a column length(L0) tall, and .* that by the result of the sum, and sum() the result of the multiplication across the first dimension. The result should be 1 x 1 x length(N0) .
Walter Roberson
Walter Roberson 2021년 2월 5일
I do not want to get involved in solving infinite numbers of linear equations. Any such a proposal is numeric nonsense, and needs to be approached through theoretical techniques, which might include:
  • "renormalization" of infinities -- the sort of mathematics that "proves" that 1-1+1+1+1... infinity "equals" 1/12
  • limit processes... which would not give you the individual values anyhow, since there are an infinite number of individual values
  • switching from summation to integration (which still will not give you all infinite number of results.)
The determinant of an infinite matrix is going to be either 0 or infinite or exactly 1. In the first two cases, you cannot find the solution for the equations; in the third case, the solution is the matrix times the marginal vector and no simultaneous equation work needs to be done.

댓글을 달려면 로그인하십시오.

카테고리

Help Center 및 File Exchange에서 Bessel functions에 대해 자세히 알아보기

태그

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by