A numerical scheme for the generalized Burgers–Huxley equation

Abstract

In this article, a numerical solution of generalized Burgers–Huxley (gBH) equation is approximated by using a new scheme: modified cubic B-spline differential quadrature method (MCB-DQM). The scheme is based on differential quadrature method in which the weighting coefficients are obtained by using modified cubic B-splines as a set of basis functions. This scheme reduces the equation into a system of first-order ordinary differential equation (ODE) which is solved by adopting SSP-RK43 scheme. Further, it is shown that the proposed scheme is stable. The efficiency of the proposed method is illustrated by four numerical experiments, which confirm that obtained 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 (non)linear physical models as compared to the earlier schemes.

Keywords

• Modified cubic B-spline
• gBH equation
• SSP-RK43 scheme
• Thomas algorithm