A numerical scheme to solve Fisher-type reaction-diffusion equations

Abstract

This article present a numerical solution of Fisher-type reaction-diffusion equation (FRDE) approximated by using a new scheme: modified cubic B-spline differential quadrature method (MCBDQM). The scheme is based on differential quadrature method where modified cubic B-splines are
used as basis functions. In this way, the FRDE is reduced into a system of first-order ordinary differential equations (ODEs), and then SSP-RK43 scheme is used to solve the resulting system of ODEs. The efficiency of the proposed method is examine by three numerical examples, it is evident that the
approximated results are in good agreement with earlier studies. This scheme is an easy, economical and efficient technique for finding numerical solutions for various kinds of linear or nonlinear physical models as compared to the earlier schemes.