A class of difference schemes uniformly convergent on a modified\n Bakhvalov mesh

2018/05/11 by Samir Karasuljić, Karasuljić, Samir, Helena Zarin +3
Engineering · Mathematics · #65L10 #65L11 #65L50 #Differential Equations and Numerical Methods #FOS: Mathematics #Material Science and Thermodynamics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1805.04298

openalex publication_date 2018/05/11 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the numerical solution of a singularly perturbed\none-dimensional semilinear reaction-diffusion problem. A class of differential\nschemes is constructed. There is a proof of the existence and uniqueness of the\nnumerical solution for this constructed class of differential schemes. The\ncentral result of the paper is an \ε--uniform convergence of the\nsecond order \O\(1/N² \), for the discrete approximate\nsolution on the modified Bakhvalov mesh. At the end of the paper there are\nnumerical experiments, two representatives of the class of differential schemes\nare tested and it is shown the robustness of the method and concurrence of\ntheoretical and experimental results.\n

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