A Numerical Treatment of Fisher Equation

Abstract

Fisher equation is commonly arises in chemistry, heat and mass transfer, biology and ecology. In mathematics Fisher equation is also known as Kolmogorov Petrovsky-Piscounov equation, KPP equation or Fisher KPP equation. Fisher equation describes the process of interaction between diffusion and reaction. In this paper a semi implicit method is used to solve the Fisher equation. A semi implicit finite difference scheme has been designed for numerical solution of one dimensional nonlinear Fisher equation. The designed scheme accuracy is first order in time and second order in space. Numerical results are calculated for different values of Diffusion coefficient and time steps are matching with exact solution.