Publication:
A uniformly convergent scheme to solve two-dimensional parabolic singularly perturbed systems of reaction-diffusion type with multiple diffusion parameters

Date

2021

Authors

Director

Publisher

John Wiley & Sons Ltd
Acceso cerrado / Sarbide itxia
Artículo / Artikulua

Project identifier

Métricas Alternativas

Abstract

In this work, we deal with solving two-dimensional parabolic singularly perturbed systems of reaction-diffusion type where the diffusion parameters at each equation of the system can be small and of different scale. In such case, in general, overlapping boundary layers appear at the boundary of the spatial domain and, because of this, special meshes are required to resolve them. The numerical scheme combines the central difference scheme to discretize in space and the fractional implicit Euler method together with a splitting by components to discretize in time. If the fully discrete scheme is defined on an adequate piecewise uniform Shishkin mesh in space then it is uniformly convergent of first order in time and of almost second order in space. Some numerical results illustrate the theoretical results. © 2020 John Wiley & Sons, Ltd.

Description

Alojado según Res. CNEAI 5/12/23 (ANECA)

Keywords

Fractional Euler method, Reaction diffusion parabolic systems, Shishkin meshes, Splittingby components, Uniform convergence

Department

Estadística, Informática y Matemáticas / Estatistika, Informatika eta Matematika / Institute of Smart Cities - ISC

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item.page.cita

Clavero, C., Jorge, J.C. (2021) A uniformly convergent scheme to solve two-dimensional parabolic singularly perturbed systems of reaction-diffusion type with multiple diffusion parameters. Computational and Mathematical Methods, 3(3), 1-14. https://doi.org/10.1002/cmm4.1093.

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