Implicit numerical techniques for Fisher equation

Abstract

A very common known equations which is having higher level of significance in biology, chemistry, ecology and heat transfer is Fisher equation. Fisher equation is described as a KPP equation, Kolmogorov Petrovsky-Piscounov or Fisher KPP equation in mathematics. Fisher equation is a kind of partial differential equation which is nonlinear in nature of second order with nonlinear source term and this PDE have combined effects of interaction in between reactions and diffusions involved in physical phenomenon. Two implicit methods have been suggested in the paper presented to get the solution of Fisher equation. This methods are based on a semi implicit finite difference scheme. First scheme is modified CN method and second one is modified Keller Box and both the designed schemes having accuracy of second order in both time and space. The one major advantage of the designed schemes is that both are unconditionally stable. Numerical results have been calculated for the mentioned example at different values of coefficient of diffusion at various time and space steps which gives satisfactory results with exact solution.