TITLE:
Numerical Study of One Dimensional Fishers KPP Equation with Finite Difference Schemes
AUTHORS:
Shahid Hasnain, Muhammad Saqib
KEYWORDS:
Forward in Time and Centre in Space (FTCS), Lax Wendroff, Taylor’s Series, Crank Nicolson and Richardson Extrapolation
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.7 No.1,
March
31,
2017
ABSTRACT: In this paper, we originate results with finite difference schemes to
approximate the solution of the classical Fisher Kolmogorov Petrovsky Piscounov
(KPP) equation from population dynamics. Fisher’s equation describes a balance
between linear diffusion and nonlinear reaction. Numerical example illustrates
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.