AUTHOR=Derzie Eshetu B. , Munyakazi Justin B. , Dinka Tekle G. TITLE=A NSFD method for the singularly perturbed Burgers-Huxley equation JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=9 YEAR=2023 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2023.1068890 DOI=10.3389/fams.2023.1068890 ISSN=2297-4687 ABSTRACT=

This article focuses on a numerical solution of the singularly perturbed Burgers-Huxley equation. The simultaneous presence of a singular perturbation parameter and the nonlinearity raise the challenge of finding a reliable and efficient numerical solution for this equation via the classical numerical methods. To overcome this challenge, a nonstandard finite difference (NSFD) scheme is developed in the following manner. The time variable is discretized using the backward Euler method. This gives rise to a system of nonlinear ordinary differential equations which are then dealt with using the concept of nonlocal approximation. Through a rigorous error analysis, the proposed scheme has been shown to be parameter-uniform convergent. Simulations conducted on two numerical examples confirm the theoretical result. A comparison with other methods in terms of accuracy and computational cost reveals the superiority of the proposed scheme.