Inversion of multi-dimensional Laplace transforms-analytical and numerical techniques
M. W. Smiley
In the first part of this dissertation we establish several new theorems in multidimensional inverse Laplace transforms. These results are derived from the known results of the one-dimensional Laplace transforms by using operational techniques. These theorems are applied to a number of commonly used special functions to derive new two-dimensional transform pairs;In Part II, we develop two algorithms to numerically invert two-dimensional Laplace transforms. One of the methods is based on expanding the inverse function in a series of products of (generalized) Laguerre polynomials. This method is an extension of the method presented by Weeks and the generalized version suggested by Luke and implemented by Piessens and Branders for the one-dimensional inverse Laplace transforms. The other method uses the finite Fourier Cosine and Sine series to approximate the inverse integral. This method is an extension of the method first presented by Dubner and Abate and later improved by Crump for one-dimensional problems.