Path-following methods for boundary value problems and their applications to combustion equations : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University

Abstract

This thesis is primarily concerned with the numerical techniques involved in bifurcation analysis, in particular with the software package AUTO developed by Eusebius Doede! which performs this analysis on dynamical systems.

The techniques of AUTO are investigated and applied to a steady state heat equation. The chosen equation can be solved by analytical methods for some boundary conditions. Initially AUTO was successfully applied to such problems, which have analytical solutions confirming its reliability. The software was then used to solve dynamical system problems which do not have known analytical solutions. These problems necessitated a modification to AUTO for non-autonomous systems. The modified version of AUTO was shown to be successful in finding solutions to these problems.