PDE

The goal of this blog is to understand how Melnikov theory can be used to determine the wavespeed of travelling waves in a perturbed reaction-diffusion system. In particular the focus of this blog will be on the paper Wavespeed in reaction-diffusion systems, with application to chemotaxis and population pressure (Balasuriya and Gottwald 2010). We wish to investigate perturbing a standard form of a reaction-diffusion partial differential equation (PDE) which allows us to use tools from Melnikov method to find the wavespeed of the solution....

Method of lines is a numerical technique used to solve a large class of partial differential equations (PDEs). Method to lines uses finite differences methods by discretising all spatial variables of a PDE while time remains continuous. This results in a system of ordinary differential equations (ODEs) which can be solve numerically using solvers such as ode15s() in Matlab. One prime example of a PDE encountered by many undergraduate students is the diffusion equation....