3D numerical integration error

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dont panic 2013-9-24

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https://ww2.mathworks.cn/matlabcentral/answers/88116-3d-numerical-integration-error

Hello,

i have writen a short code for the integration of a 2D integration field with 3 independent integration parameters and at a few points i get the following error message:

"Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 2.7e+00. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy."

The integral code is as follows:

for k=1 : numel(mp)

    k
     f= @(r,phi,z)((Z(k)-z).*r)./(R(k)^2-2.*r*R(k).*cos(phis-phi)+r.^2+(Z(k)-z).^2).^(3/2);
    mp(k)=integral3(f,R1,R2,phi1,phi2,Z1,Z2,'AbsTol',1e-1,'RelTol',1e-1,'Method','iterated');

end

i haven't copied the whole script as it is not very well structured but the rest works and i have of course defines the integration boundaries (R1,R2...) before.

Thank you in advance

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Mike Hosea 2013-9-24

Well, you didn't supply any data for the parameters, so I made some up and had no trouble. Perhaps for some particular values of R(k), phis, Z(k), R1, R2, phi1, phi2, Z1, and Z2, that you have a singularity that is too strong for the code to integrate. If you supply the values for all the parameters in just one problem integration, perhaps someone can identify the problem.

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