Inversion of Division of Bessel Functions in Laplace Domain?

[ntran26]

Hello all,

I am trying to take the inversion of this function that is in Laplace domain. I've tried using a wolfram alpha solver, and I know I can probably use stehfest algorithm to numerically solve it but wanted to know if there was an exact solution.

the function is
http://www5a.wolframalpha.com/Calculate/MSP/MSP25381bbadecf0c1g821e00005285e957ic1ahh6c?MSPStoreType=image/gif&s=14&w=122.&h=52.

where Ko is the modified bessel function of the second kind with order 0, and a and b are constants. Any reference to papers would also be nice if they are out there!

Thanks

 

[jvicens]

for your question!

The inverse Laplace transform of this function does not have a closed form solution. However, there are several numerical methods that can be used to approximate the inverse. As you mentioned, the Stehfest algorithm is one option. Other methods include the Durbin method and the Talbot method.

As for references, I would recommend looking into the book "Numerical Inversion of Laplace Transforms" by Ian N. Sneddon. It provides a comprehensive overview of various numerical methods for inverse Laplace transforms and includes many examples and applications.

Additionally, you may also find some relevant papers by searching for "inverse Laplace transform of modified Bessel functions" or a similar variation on that phrase. Some potential papers that may be helpful include "A Numerical Method for Inverse Laplace Transform of Modified Bessel Functions" by S. Gorodetsky and "A Numerical Inversion Algorithm for Laplace Transforms of Modified Bessel Functions" by G. E. Fasshauer and R. Schaback.

I hope this helps and good luck with your research!