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Solution of nonlinear equations and computation of multiple solutions of a simple reaction-diffusion equation

Published online by Cambridge University Press:  17 February 2009

Adrian Swift  and
Easwaran Balakrishnan
Adrian Swift
Affiliation:
Department of Mathematics, Massey University, Albany, New Zealand.
Easwaran Balakrishnan
Affiliation:
Department of Mathematics, Massey University, Palmerston North, New Zealand.
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Abstract

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The first part of this paper starts with a brief discussion of some methods for solution of nonlinear equations which have interested the first author over the last twenty years or so. In the second part we discuss a recent research involvement, the success of which relies heavily on the numerical solution of nonlinear equation systems. We briefly describe path-following methods and then present an application to a simple steady-state reaction-diffusion equation arising in combustion theory. Results for some regular geometric shapes are shown and compared with those from an approximate method.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 1 , July 2000 , pp. 55 - 64
Copyright
Copyright © Australian Mathematical Society 2000

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