Semi-analytical solutions for reaction diffusion equations
Doctor of Philosophy
School of Mathematics and Applied Statistics
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. http://ro.uow.edu.au/theses/4478
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.