Numerical integration of double integral with two variables
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Hi,
I am trying to numerically integrate the following double integral in MATLAB:

where Im is the imaginary part of expression, i is the imaginary number, x and y are variables while a, b, and c are constants.
Here is my attempt to solve this.
a = 3;
b = 4;
c = 5;
innerintegral = @(x) integral(@(y) (1i.*x.*y)./(y.^a-1i.*x),0,6);
outerintegral = integral(@(x) imag(exp(-1i.*x.*c+b.*innerintegral(x))),0,inf, 'ArrayValued', 1);
Is this the correct way of applying numerical integration with more than one variable? Also I am getting a warning when I run this expression which reads as "Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 6.7e+00. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy."
Can anyone please validate if the above implementation is a correct way of implementing the expressions state above.
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Answers (1)
David Hill
on 2 Sep 2020
Edited: David Hill
on 2 Sep 2020
a = 3;
b = 4;
c = 5;
syms x y;
fun = @(x,y)(1i.*x.*y)./(y.^a-1i.*x);
I=vpaintegral(@(x)imag(exp(-1i.*x.*c+b.*vpaintegral(fun,y,0,6))),x,0,inf);
I get:
I= -0.0125514
3 Comments
David Hill
on 3 Sep 2020
Runs fine with the following a,b,c constants. Not sure why the other constants are causing problems.
a = 3;
b = 4;
c = 5;
syms x y;
fun = @(x,y)(1i.*x.*y)./(y.^a-1i.*x);
I=vpaintegral(@(x)imag(exp(-1i.*x.*c+b.*vpaintegral(fun,y,0,6))./x),x,0,inf);
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