American Journal of Computational Mathematics, 2017, 7, 70-83 http://www.scirp.org/journal/ajcm ISSN Online: 2161-1211 ISSN Print: 2161-1203 DOI: 10.4236/ajcm.2017.71006 March 31, 2017 Numerical Study of One Dimensional Fishers KPP Equation with Finite Difference Schemes Shahid Hasnain, Muhammad Saqib, Daoud Suleiman Mashat Department of Mathematics, Numerical Analysis, King Abdulaziz University, Jeddah, KSA Abstract In this paper, we originate results with finite difference schemes to approx- imate the solution of the classical Fisher Kolmogorov Petrovsky Piscounov (KPP) equation from population dynamics. Fisher’s equation describes a bal- ance between linear diffusion and nonlinear reaction. Numerical example il- lustrates the efficiency of the proposed schemes, also the Neumann stability analysis reveals that our schemes are indeed stable under certain choices of the model and numerical parameters. Numerical comparisons with analytical solution are also discussed. Numerical results show that Crank Nicolson and Richardson extrapolation are very efficient and reliably numerical schemes for solving one dimension fisher’s KPP equation. Keywords Forward in Time and Centre in Space (FTCS), Lax Wendroff, Taylor’s Series, Crank Nicolson and Richardson Extrapolation 1. Introduction Fisher gives introduction to nonlinear evolution equation to inquisitive, the pro- liferation of an beneficial gene in a population dynamics [1]. Fisher’s equation also specify the logistic diffusion process [1]. It has the form ( ) 1 t xx u u u u β α = + − (1) where 0 β > is a diffusion constant with 0 α > is the linear growth rate [1]. The reaction diffusion Equation (1) also express a model equation for the evo- lution of a neutron population in a nuclear reactor [2] and also appears in chemical engineering applications [2]. This equation accommodates the effects of linear diffusion along xx u and nonlinear local multiplication or reaction along ( ) 1 u u − [3] [4]. It has become one of the most important nonlinear equations and occurs in many biological and chemical processes [4] [5]. Recently, many researcher are working on this type of model to understand growth rate How to cite this paper: Hasnain, S., Saqib, N. and Mashat, S. (2017) Numerical Study of One Dimensional Fishers KPP Equation with Finite Difference Schemes. American Journal of Computational Mathematics, 7, 70-83. https://doi.org/10.4236/ajcm.2017.71006 Received: December 30, 2016 Accepted: March 28, 2017 Published: March 31, 2017 Copyright © 2017 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access