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

Question

Martin 2023-3-8

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1925090-numerical-integration-of-a-nested-integral-limits-of-inner-integral-depend-on-the-outer-integration

评论： Martin 2023-3-8

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);

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Torsten 2023-3-8

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1925090-numerical-integration-of-a-nested-integral-limits-of-inner-integral-depend-on-the-outer-integration#answer_1188335

编辑：Torsten 2023-3-8

在 MATLAB Online 中打开

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
显示 -1更早的评论隐藏 -1更早的评论

Martin 2023-3-8

在 MATLAB Online 中打开

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