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Titolo
Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions.
Autor(es)
Soggetto
Boundary layers
Robin boundary conditions
Adaptive mesh
Equidistribution principle
Fecha de publicación
2021
Editore
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.
URI
ISSN
0096-3003
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