A uniformly convergent scheme to solve two-dimensional parabolic singularly perturbed systems of reaction-diffusion type with multiple diffusion parameters
Fecha
2021Versión
Acceso cerrado / Sarbide itxia
Tipo
Artículo / Artikulua
Impacto
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10.1002/cmm4.1093
Resumen
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 sch ...
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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. [--]
Materias
Fractional Euler method,
Reaction diffusion parabolic systems,
Shishkin meshes,
Splittingby components,
Uniform convergence
Editor
John Wiley & Sons Ltd
Publicado en
Computational and Mathematical Methods, 3(3), 1-14
Notas
Alojado según Res. CNEAI 5/12/23 (ANECA)
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute of Smart Cities - ISC