Numerical integration of double integral

Dear all,

I am trying to numerically integrate the following double integral but have come across resistance:

It should be noted that similar questions have already been posed and answered in MATLAB Answers, but when I tried applying one of them (specifically, see the accepted answer https://www.mathworks.com/matlabcentral/answers/127087-using-integral2-on-a-matrix-with-function-handler-components#answer_134468), I get the error message that "A and B must be floating point scalars".

Here is my attempt to solve this.

y1min = 0;
y2min = @(y1) y1;
f1 = @(y1,y2) integral(@(x) x/(1+x^alpha/(0.1*y1+1.1*y2)),y2,Inf,'ArrayValued',1);
f2 = @(y1,y2) exp(-2*pi*f1(y1,y2)) * exp(-pi*y2^2)*y1*y2;
f3 = @(y1) integral(@(y2) f2(y1,y2),y2min,Inf,'ArrayValued',1);
res = integral(@(y1) f3(y1),y1min,Inf,'ArrayValued',1),

PS. It would be nice if the solution method that is in the end applied is flexible enough since I also plan to numerically integrate a triple integral later on.

Many thanks for your help.

[Gunnar]

No answers so far...

Anyone with any idea? Help is greatly appreciated!

Answer 1

[Ameer Hamza]

Try this

f1 = @(y1,y2) integral(@(x) x./(1+x.^4/(0.1*y1.^4+1.1*y2.^4)),y2,Inf);
f2 = @(y1,y2) exp(-2*pi*f1(y1,y2)) * exp(-pi*y2^2)*y1*y2;
f3 = @(x) integral(@(y) f2(x,y), x, inf, 'ArrayValued', 1);
result = integral(f3, 0, inf, 'ArrayValued', 1);

To extend it to triple integral, just look at how f3 and result statement are related to each other.

[Gunnar]

Thanks very much for your answer!

Can you please explain the meaning of 0.2 in f2(0.2,y)?

[Ameer Hamza]

Sorry!!! That was an error. I was testing it in MATLAB and pasted a wrong statement here. I have modified the answer.

[Gunnar]

Seems to be working! :)

Thanks very much! I will accept your answer.

[Ameer Hamza]

You are welcome.