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Titre
A rapidly converging domain decomposition algorithm for a time delayed parabolic problem with mixed type boundary conditions exhibiting boundary layers.
Autor(es)
Sujet
Delay differential equations
Singularly perturbed problems
Uniformly convergent methods
Domain decomposition methods
Parabolic problems
Fecha de publicación
2024
Éditeur
Springer
Citación
Aakansha, Kumar, S. & Ramos, H. A rapidly converging domain decomposition algorithm for a time delayed parabolic problem with mixed type boundary conditions exhibiting boundary layers. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-01987-8
Resumen
[EN]A rapidly converging domain decomposition algorithm is introduced for a time delayed parabolic problem with mixed type boundary conditions exhibiting boundary layers. Firstly, a space-time decomposition of the original problem is considered. Subsequently, an iterative process is proposed, wherein the exchange of information to neighboring subdomains is accomplished through the utilization of piecewise-linear interpolation. It is shown that the algorithm provides uniformly convergent numerical approximations to the solution. Our analysis utilizes some novel auxiliary problems, barrier functions, and a new maximum principle result. More importantly, we showed that only one iteration is needed for small values of the perturbation parameter.
URI
ISSN
1598-5865
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1.120Mo
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