How to do numerical 4-fold integral (more than triple) by using matlab?

조회 수: 7 (최근 30일)
sun
sun 2015년 1월 5일
답변: sun 2015년 1월 6일
Dear friend, My question is that how to do the 4-fold integration. I use to want to do more that 5-fold, but I failed..... so, I decide to go back to a lower level, just 4 fold numerical integration. Please check the code below, there are some parameters and one function.
clear all;
%%%=== just some parameters ==============
a=4;
la1=1/(pi*500^2); la2= la1*5;
p1=25; p2=p1/25;
sgma2=10^(-11);
index=1;
g=2./a;
syms r u1 u2 u3 u4
powe= 0 ;
seta= 10^powe;
q=pi.*(la1.*p1.^(2./a)+la2.*p2.^(2./a));
%%%=== just some parameters END here ==============
%%%=== Function I want to do 4-fold numerical integration below ===
yi = exp(-u3.*(1+2.*...
( out1 )./...
( (( (u3./u1).^(a./2) + (u3./u2).^(a./2) + 1 ).^(2./a)).*seta.^(-2./a)))).*...
exp(-sgma2.*q.^(-a./2).* seta.*u3.^(a./2)./...
((( (u3./u1).^(a./2) + (u3./u2).^(a./2) + 1 ).^(2./a)).^(a./2)) );
Ok, As you seen, variables are u1,u2,u3,u4. There will be 4 'nest' integration. The most inside variable is u1, 2nd is u2, 3rd is u3, the most outside is u4. The range of u1 is [0, u2], u2 is [0, u3], u3 is [0, u4], u4=[0, Inf]. This is a numerical integration, this means after 4 level numerical integration, the final output is a real number, not a symbol.
Thank you so much for your time. Thanks. %%%%%====================================================================== The information below is what I've tried.
In another "try-version" of my code, yi is only function of u1, u2. and if I use int 2 times as below,
%%= 1000 means Inf here, 1st int var is u1 and range is[0 u2], 2nd int var is w.r.t u2 and [0, 1000 or Inf]
out2 = double ( int(int(yi,u1,0,u2),u2, 0 ,1000))
For the code above, it's working! it gave me a real number. Then I want to try 3 fold, If I do the same thing for 3 fold integration, I failed. So, I change yi to function of u1,u2,u3. and I do code below,
out2 = double ( int(int(int(yi,u1,0,u2),u2, 0 ,u3)),u3,0,inf)
1st var is u1, range is [0 u2]; 2nd var is u2, the range is [0 u3]; last one is u3, [0 Inf]. error from above code is
Warning: Explicit integral could not be found.
Warning: Explicit integral could not be found.
Warning: Explicit integral could not be found.
Error using sym/double
Too many input arguments.
Error in ref7_equ11n2 (line 117)
out2 = double ( int(int(int(yi,u1,0,u2),u2, 0 ,u3)),u3,0,inf)
As you seen, I am not using quad2d, integral3 or other in-built functions. Because I know I will get a 'right' answer for 2 or 3 fold integration. But my target is for 4-fold. that's why I need to do it in 'int' way, step by step. Thank you.
  댓글 수: 4
sun
sun 2015년 1월 5일
Dear John, could you say it more clear? I am not very follow you. So, which function is right one to do this 4-fold intergration? Thank you,
sun
sun 2015년 1월 5일
편집: sun 2015년 1월 6일
Well, If I put a vpa before double, I will have the right answer for 3-fold integration. It's also working for 4-fold integration. thanks guys

댓글을 달려면 로그인하십시오.

채택된 답변

sun
sun 2015년 1월 6일
Well, If I put a vpa before double, I will have the right answer for 3-fold integration. It's also working for 4-fold integration. thanks guys

추가 답변 (0개)

카테고리

Help CenterFile Exchange에서 Numeric Solvers에 대해 자세히 알아보기

Community Treasure Hunt

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

Start Hunting!

Translated by