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Help with double numerical integration (Inverse Fourier and Laplace Transforms)

POSTED BY: Daniel Urbanski
4 Replies

I really like the formatting you have provided here, it is very helpful and transparent. I can't seem to get a simple expression to work with it, however. My take away is that it's not going to be possible to do a double integral in this way. For example, for the following function f:

g/((g^2 + w0^2) (DiracDelta[\[Theta]-1]+DiracDelta[\[Theta]+1])

The inversions should yield cosines, however the integrals provide the errors: NInverseLaplaceTransform::wrongexpr: The argument invFT[g,0.2] is not Numeric at fixed g .

I think the approach should be as you said in your previous comment. I need to conduct the first integral symbolically and then I can do it numerically for the second variable. Thanks again for your help!

POSTED BY: Daniel Urbanski

Thank you for response! I had done that method previously and for the function I provided the symbolic method works quite well. I had hoped to use the double numerical method to solve a more complex expression and since I knew this one could be handled symbolically I thought it would be a good test to try numerically, but I see why that isn't the case. Thanks again, apologies for the delated response!

POSTED BY: Daniel Urbanski
POSTED BY: Gianluca Gorni

Your function f[g, s, \[Omega]0, k0, \[Theta]] is not integrable with respect to \[Theta]. My understanding is that NInverseFourierTransform relies on numerical integration, which is likely to fail. Try the symbolic way, which handles non-integrable cases:

InverseFourierTransform[f[g, s, \[Omega]0, k0, \[Theta]],
 \[Theta], \[Omega]]
POSTED BY: Gianluca Gorni
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