A NSFD method for the singularly perturbed Burgers-Huxley equation
Date
2023Author
Derzie, Eshetu B.
Munyakazi, Justin B.
Dinka, Tekle G.
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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.