Reaction-Diffusion equations are often used as simplified models to study the emergence of patterns in nature. In this thesis we explore how numerical methods can be used to compute solutions of...Show moreReaction-Diffusion equations are often used as simplified models to study the emergence of patterns in nature. In this thesis we explore how numerical methods can be used to compute solutions of Reaction-Diffusion equations that resemble patterns. In the first part we focus on numerical methods in the context of ODEs, in particular the forward Euler and fourth-order Runge-Kutta methods. To then study numerical methods for PDEs, in particular how to discretize the Laplacian via a finite difference method. In the second part we turn our attention to the numerical construction of pattern solution via the use of numerical continuation. We study the concepts of numerical continuation again first for ODEs and then use the Matlab package pde2path to determine patterns of a Reaction-Diffusion equation. The main novelty is a numerical study of the effect of inhomogenous terms on pattern solutions.Show less
