Finite difference method for numerical solution of a generalized burgers-huxley equation

Abstract

There are many applications of the generalized Burgers-Huxley equation which is a form of nonlinear Partial Differential Equation such as in the work of physicist which can effectively models the interaction between reaction mechanisms, convection effects and diffusion transports. This study investigates on the implementation of numerical method for solving the generalized Burgers-Huxley equation. The method is known as the Finite Difference Method which can be employed using several approaches and this work focuses on the Explicit Method, the Modified Local Crank-Nicolson (MLCN) Method and Nonstandard Finite Difference Schemes (NFDS). In order to use the NFDS, due to a lack of boundary condition provided in the problem, this research used the Forward Time Central Space (FTCS) Method to approximate the first step in time. Thomas Algorithm was applied for the methods that lead to a system of linear equation. Computer codes are provided for these methods using the MATLAB software. The results obtained are compared among the three methods with the exact solution for determining their accuracy. Results shows that NFDS has the lowest relative error and one of the best way among these three methods in order to solve the generalized Burgers-Huxley equations.