Numerical laplace inversion of (s²+a²)^−(n+½)(s²+b²)^−m

Abstract

A numerical method is developed for the computation of a function H _mn (t) which is the Laplace-inverse function of (s ²+a ²)^−(n−½)(s ²+b ²)^−m The method consists of expanding the function H _mn (t) in a series whose typical term is associated with a Bessel-like functions G _i (a t).

A simple technique, suitable for the purpose, is developed for the computation of the function G _i (a t).

A few typical results for H _mn (t) are given.

Keywords:

• Algorithm
• numerical computation
• Bessel-like functions
• Laplace-inverse
• irrational functions

C.R. Categories:

• G.1.0
• J2
• G.1.m