Comparing numerical methods for solving the Fisher equation

Abstract

This thesis provides a comparison of results from Finite Difference Methods, pdepe solver and the Method of Lines when solving the Fisher equation and the heat equation. We study the Fisher equation, which is an example of the parabolic equation and the heat equation as a special case of the Fisher equation. We compute the numerical solutions of the two parabolic equations using the FDMs, the pdepe MATLAB solver and the MOLs and compare their results with the analytical solutions at different times. Finally the CPU time and the accuracy were computed and presented when solving these parabolic equations.