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Título
Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions.
Autor(es)
Palabras clave
Boundary layers
Robin boundary conditions
Adaptive mesh
Equidistribution principle
Fecha de publicación
2021
Editor
Elsevier
Citación
Sunil Kumar, Sumit, Higinio Ramos, Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions, Applied Mathematics and Computation, Volume 392, 2021, 125677, ISSN 0096-3003, https://doi.org/10.1016/j.amc.2020.125677. (https://www.sciencedirect.com/science/article/pii/S0096300320306305)
Resumen
[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.
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ISSN
0096-3003
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