Degree Type

Dissertation

Date of Award

1990

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

R. S. Dahiya

Second Advisor

M. W. Smiley

Abstract

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.

DOI

https://doi.org/10.31274/rtd-180813-9421

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Manickavasagar Vinayagamoorthy

Language

en

Proquest ID

AAI9110576

File Format

application/pdf

File Size

196 pages

Included in

Mathematics Commons

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