Numerical Solution of Burgers–Huxley Equation Using a Higher Order Collocation Method

Abstract

In this paper, the collocation method with cubic B-spline as basis function has been successfully applied to numerically solve the Burgers–Huxley equation. This equation illustrates a model for describing the interaction between reaction mechanisms, convection effects, and diffusion transport. Quasi-linearization has been employed to deal with the nonlinearity of equations. The Crank–Nicolson implicit scheme is used for discretization of the equation and the resulting system turned out to be semi-implicit. The stability of the method is discussed using Fourier series analysis (von Neumann method), and it has been concluded that the method is unconditionally stable. Various numerical experiments have been performed to demonstrate the authenticity of the scheme. We have found that the computed numerical solutions are in good agreement with the exact solutions and are competent with those available in the literature. Accuracy and minimal computational efforts are the key features of the proposed method.