Numerical Treatment of Burger-Fisher Equation

Abstract

Nonlinear partial differential equations are encountered in the various field of science. Generalized Burger Fisher equation is of high importance for describing different mechanisms. Burgers-Fisher equation arises in field of financial mathematics, gas dynamics, traffic flow, applied mathematics and physics applications. This equation shows a prototypical model for describing the interaction between the reaction mechanisms, convection effect, and diffusion transport. In this paper two implicit methods are used to solve the Burger-Fisher equation. Two implicit finite difference schemes has been designed for numerical solution of one dimensional nonlinear Burgers- Fisher equation. Numerical results are calculated for different values of constants and time steps are matching with exact solution. Order of accuracy and error analysis is also carried out for Burgers-Fisher equation.