Numerical solutions of nonlinear Burgers‒Huxley equation through the Richtmyer type nonstandard finite difference method

Document Type : Research Paper

Authors

1 Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran

2 Department of applied mathematics, Faculty of mathematical sciences, Lahijan branch, Islamic Azad University, Lahijan, Iran

3 Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran.

10.22075/ijnaa.2021.25004.2878

Abstract

The Burger‒Huxley equation as a well-known nonlinear physical model is studied numerically in the present paper. In this respect, the nonstandard finite difference (NSFD) scheme in company with the Richtmyer’s (3, 1, 1) implicit formula is formally adopted to accomplish this goal. Moreover, the stability, convergence, and consistency analyses of nonstandard finite difference schemes are investigated systematically. Several case studies with comparisons are provided, confirming that the current numerical scheme is capable of resulting in highly accurate approximations.

Keywords