A numerical approach for solving Fisher’s reaction–diffusion equation via a new kind of spline functions

Abstract

The objective of this work is to propose a hybrid numerical method for the approximation of Fisher’s reaction–diffusion equation. The method is based on cubic uniform algebraic trigonometric (CUAT) tension B-spline functions and differential quadrature method (DQM). Using CUAT tension B-spline, the weighting coefficients are calculated in DQM which reduces the Fisher’s reaction–diffusion equation to a system of ODEs. An optimal SSP-RK54 method is used for solving the resulting ODEs. Four examples are considered in order to compare the present results with analytical and existing numerical results. It is observed that the proposed method is not only quite easy to implement, but it also provides better results. The stability analysis is also discussed.

Keywords

• Fisher’s reaction–diffusion equation
• CUAT tension B-spline functions
• DQM
• SSP-RK54
• Stability analysis