Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions.

[EN]In this work we develop a parameter-uniform numerical method on equidistributed meshes for solving a class of singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions. The discretization consists of a modified Euler scheme in time, a central difference scheme in...

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Detalles Bibliográficos
Autores: Kumar, Sunil, Sumit, Null, Ramos Calle, Higinio
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Universidad de Salamanca (USAL)
Repositorio:GREDOS. Repositorio Institucional de la Universidad de Salamanca
OAI Identifier:oai:gredos.usal.es:10366/156978
Acceso en línea:http://hdl.handle.net/10366/156978
Access Level:acceso abierto
Palabra clave:Boundary layers
Robin boundary conditions
Adaptive mesh
Equidistribution principle
Descripción
Sumario:[EN]In this work we develop a parameter-uniform numerical method on equidistributed meshes for solving a class of singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions. The discretization consists of a modified Euler scheme in time, a central difference scheme in space, and a special finite difference scheme for the Robin boundary conditions. A uniform mesh is used in the time direction while the mesh in the space direction is generated via the equidistribution of a suitably chosen monitor function. We discuss error analysis and prove that the method is parameter-uniformly convergent of order two in space and order one in time. To support the theoretical result, some numerical experiments are performed.