Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations

Author:

Kabeto Masho Jima,Duressa Gemechis File

Abstract

Abstract Objective The main purpose of this paper is to present an accelerated nonstandard finite difference method for solving the singularly perturbed Burger-Huxley equation in order to produce more accurate solutions. Results The quasilinearization technique is used to linearize the nonlinear term. A nonstandard methodology of Mickens procedure is used in the spatial direction and also within the first order temporal direction that construct the first-order finite difference approximation to solve the considered problem numerically. To accelerate the rate of convergence from first to second-order, the Richardson extrapolation technique is applied. Numerical experiments were conducted to support the theoretical results.

Publisher

Springer Science and Business Media LLC

Subject

General Biochemistry, Genetics and Molecular Biology,General Medicine

Reference14 articles.

1. Bullo T, Duressa GF, Degla G. Accelerated fitted operator finite difference method for singularly perturbed parabolic reaction-diffusion problems. Computat Methods Diff Eq. 2021;9(3):886–98.

2. Bullo TA, Degla GA, Duressa GF. Uniformly convergent higher-order finite difference scheme for singularly perturbed parabolic problems with non-smooth data. J Appl Math Comput Mech. 2021;20(1):5–16.

3. Mekonnen TB, Duressa GF. A computational method for singularly perturbed two-parameter parabolic convection-diffusion problems. Cogent Math Stat. 2020;7(1):1829277.

4. Bullo TA, Duressa GF, Degla GA. Robust finite difference method for singularly perturbed two-parameter parabolic convection-diffusion problems. Int J Comput Methods. 2021;18(2):2050034.

5. Woldaregay MM, Duressa GF. A uniformly convergent numerical method for singularly perturbed delay parabolic differential equations arising in computational neuroscience. Kragujevac J Math. 2022;46(1):65–84.

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