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Título
Robust numerical schemes for time delayed singularly perturbed parabolic problems with discontinuous convection and source terms.
Autor(es)
Materia
Singular perturbation
Time delay Interior layer
Semilinear parabolic problem
Error analysis
Clasificación UNESCO
12 Matemáticas
Fecha de publicación
2023
Editor
Springer
Citación
Priyadarshana, S., Mohapatra, J. & Ramos, H. Robust numerical schemes for time delayed singularly perturbed parabolic problems with discontinuous convection and source terms. Calcolo 61, 1 (2024). https://doi.org/10.1007/s10092-023-00552-2
Resumen
[EN]This article deals with two different numerical approaches for solving singularly perturbed parabolic problems with time delay and interior layers. In both approaches, the implicit Euler scheme is used for the time scale. In the first approach, the upwind scheme is used to deal with the spatial derivatives whereas in the second approach a hybrid scheme is used, comprising the midpoint upwind scheme and the central difference scheme at appropriate domains. Both schemes are applied on two different layer resolving meshes, namely a Shishkin mesh and a Bakhvalov–Shishkin mesh. Stability and error analysis are provided for both schemes. The comparison is made in terms of the maximum absolute errors, rates of convergence, and the computational time required. Numerical outputs are presented in the form of tables and graphs to illustrate the theoretical findings.
URI
ISSN
0008-0624
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