Second-Order Robust Numerical Method for a Partially Singularly Perturbed Time-Dependent Reaction–Diffusion System.
[EN]This article aims at the development and analysis of a numerical scheme for solving a singularly perturbed parabolic system of n reaction–diffusion equations where m of the equations (with <) contain a perturbation parameter while the rest do not contain it. The scheme is based on a uniform m...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/156290 |
| Acceso en línea: | http://hdl.handle.net/10366/156290 |
| Access Level: | acceso abierto |
| Palabra clave: | Singular perturbation Time-dependent reaction–diffusion Boundary layers phenomena System of equations Shishkin mesh Parameter-uniform convergence 12 Matemáticas |
| Sumario: | [EN]This article aims at the development and analysis of a numerical scheme for solving a singularly perturbed parabolic system of n reaction–diffusion equations where m of the equations (with <) contain a perturbation parameter while the rest do not contain it. The scheme is based on a uniform mesh in the temporal variable and a piecewise uniform Shishkin mesh in the spatial variable, together with classical finite difference approximations. Some analytical properties and error analyses are derived. Furthermore, a bound of the error is provided. Under certain assumptions, it is proved that the proposed scheme has almost second-order convergence in the space direction and almost first-order convergence in the time variable. Errors do not increase when the perturbation parameter →0, proving the uniform convergence. Some numerical experiments are presented, which support the theoretical results. |
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