Numerical integration of a nested integral; limits of inner integral depend on the outer integration variable

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Martin
Martin 2023-3-8
评论： Martin 2023-3-8
Ran in:
I have 2 nested integrals. I want to integrate a bessel function multiplied by x. And the integration limits depend on the integration variable of the outer intergral.
The outer integral should go till inf. But for simplification i set it to 1e6.
The following code is a example code, which doesnt work. because the integration limits arent scalar values.
This integral doesnt habe a analytical solution so i cant simplify it.
How can i change my implementation to solve this problem?
Thank you!
Bessel_integrand = @(x) x .* besselj(0,x);
Integrand_B = @(a) integral(Bessel_integrand,a * 1, a * 2);
result = integral ( Integrand_B, 0 , 1e6);
Error using integral
Limits of integration must be double or single scalars.

Error in solution (line 2)
Integrand_B = @(a) integral(Bessel_integrand,a * 1, a * 2);

Error in integralCalc/iterateScalarValued (line 314)
fx = FUN(t);

Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)
[q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 87)
Q = integralCalc(fun,a,b,opstruct);

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回答（1 个）

Torsten
Torsten 2023-3-8
编辑：Torsten 2023-3-8
Ran in:
I'm not sure your integral exists ...
Bessel_integrand = @(x) x .* besselj(0,x);
Integrand_B = @(a) integral(Bessel_integrand,a, 2*a)
Integrand_B = function_handle with value:
@(a)integral(Bessel_integrand,a,2*a)
result = integral(Integrand_B,0,1000,'ArrayValued',true)
result = 17.1918
  1 个评论
Martin
Martin 2023-3-8
Ran in:
Thanks for the answer! Yes this integral doesnt exist. I forgot a very important part of my simplified code.
Now it works!
Bessel_integrand = @(x) x .* besselj(0,x);
Integrand_B = @(a) integral(Bessel_integrand,a, 2*a).^2 * 1/a^4
Integrand_B = function_handle with value:
@(a)integral(Bessel_integrand,a,2*a).^2*1/a^4
result = integral(Integrand_B,0,1000,'ArrayValued',true)
result = 1.8843

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