High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems
The orders of PDE-convergence in the Euclidean norm of s-stage AMF-W-methods for two-dimensional parabolic problems on rectangular domains are considered for the case of Dirichlet boundary conditions and an initial condition. The classical algebraic conditions for order p with p ≤ 3 are shown to be...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de La Laguna (ULL) |
| Repositorio: | RIULL. Repositorio Institucional de la Universidad de La Laguna |
| OAI Identifier: | oai:riull.ull.es:915/39034 |
| Acceso en línea: | http://riull.ull.es/xmlui/handle/915/39034 |
| Access Level: | acceso abierto |
| Palabra clave: | Parabolic problem AMF-W method PDE-convergence Order conditions Fractional order AMS subject classifications: 65M12, 65M15, 65M20 |
| Sumario: | The orders of PDE-convergence in the Euclidean norm of s-stage AMF-W-methods for two-dimensional parabolic problems on rectangular domains are considered for the case of Dirichlet boundary conditions and an initial condition. The classical algebraic conditions for order p with p ≤ 3 are shown to be sufficient for PDE-convergence of order p (independently of the spatial resolution) in the case of time-independent Dirichlet boundary conditions. Under additional conditions, PDE-convergence of order p = 3.25 − for every > 0 can be obtained. In the case of time-dependent boundary conditions the order reduction is more dramatic, but order p = 2.25 − for every > 0 can be achieved. |
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