Semi-analytical solutions for reaction diffusion equations
Year
2015
Degree Name
Doctor of Philosophy
Department
School of Mathematics and Applied Statistics
Recommended Citation
Al Noufaey, Khaled Sadoon N., Semi-analytical solutions for reaction diffusion equations, Doctor of Philosophy thesis, School of Mathematics and Applied Statistics, University of Wollongong, 2015. https://ro.uow.edu.au/theses/4478
Abstract
Semi-analytical solutions for three reaction-diffusion equation models are investigating in this thesis. The three models are the reversible Selkov, or glycolytic oscillations model, an extended Selkov model which incorporates the effects of a precursor chemical and final product and a Lotka-Volterra prey-predator system with two days.
The Galerkin method is applied, which approximates the spatial structure of the concentration or population densities. This approach is used to obtain a lower-order, ordinary differential equation model, for the system of governing equations. The semi-analytical model is analysed to obtain steady-state solutions, bifurcation diagrams and parameter maps in which the different types of birurcation patterns and Hopf bifurcations occur.
FoR codes (2008)
0102 APPLIED MATHEMATICS
Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.