Numerical solution of nonlinear diffusion advection Fisher equation by fourth‐order cubic B‐spline collocation method

Abstract

This article investigates the effect of diffusion, advection and Fisher terms when nonlinear diffusion occurs in a porous medium. The main advantage of this article is the derivation of a fourth‐order cubic B‐spline collocation method to solve the nonlinear advection‐diffusion Fisher equation, which represents many important natural phenomena. The Crank‐Nicholson method has been used to discretize space and time. The salient feature of the article is the demonstration of the unconditional stability of the proposed method using the Fourier method. While applying on existing problem having an exact solution, it is shown through error analysis that our proposed scheme is very effective. The important feature of the article is the graphical showcasing of the solution profiles for different particular cases.