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 e cient
numerical solution for this equation via the classical numericalmethods. To overcome
this challenge, a nonstandard finite dierence (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 dierential 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-uniformconvergent.
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
Mathematics, Burgers-Huxley equation, Applied Mathematics, Nonlinear equation
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. 10.3389/fams.2023.1068890