A MATLAB Method of Lines Template for Evolution Equations

Abstract

Many environmental problems involve diffusion and convection processes, which can be described by Partial Differential Equations (PDEs). This paper will describe the development of a MATLAB template that generates a numerical solution to PDEs using the Method of Lines. The template will be applied to various problems within soil physics to demonstrate the versatility of the method. In particular, the template will generate a solution for one-dimensional infiltration, and two-dimensional infiltration over a complex geometry. Where possible, the results from the template will be compared against analytical solutions to determine the accuracy of the numerical solution. In addition, the paper will provide a discussion on possible extensions to the template and future directions.