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

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 r esearch involvement, the success of which relies heavily on the numerical s olution of nonlinear equation systems. We briefly describe path-following m ethods and then present an application to a simple steady-state reaction-di ffusion equation arising in combustion theory. Results for some regular geo metric shapes are shown and compared with those from an approximate method.