A NSFD method for the singularly perturbed Burgers-Huxley equation
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Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
Frontiers Media
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.
Description
Keywords
Applied Mathematics, Burgers-Huxley equation, Nonlinear equations, Parameter-uniform convergence
Citation
Derzie, E. B. et al. (2023). A NSFD method for the singularly perturbed Burgers-Huxley equation. Frontiers in Applied Mathematics and Statistics, 9, 1068890. https://doi.org/10.3389/fams.2023.1068890