0
$\begingroup$

I need to solve a cylindrical diffusion problem that is defined in $[1,\infty]$. I would like to use Hankel Transform that has is defined on $[0,\infty]$. So in order to apply Hankel transform in my case, do I need to change the Kernel of the Transformation.

$\endgroup$
  • $\begingroup$ You probably have a condition at $r=1$. So your transform should be tailored to that condition. $\endgroup$ – DisintegratingByParts Aug 9 '18 at 17:38
1
$\begingroup$

Yes, you do.

In general, the Bessel solutions to the boundary value problem require that the function remains finite at r = 0.

If your domain does not include r = 0 (and yours does not!) then you need to use a linear combination of Bessel functions of the first, and second kind.

A bit of Googling will help you to get a good idea about how to go about this. For example, "Theory and Operational Rules for the Discrete Hankel Transform" is a very nice paper which attempts to put the DHT on equal footing with the discrete Fourier transform.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.