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...

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Detalles Bibliográficos
Autores: Gonz´alez-Pinto, Severiano, Hairer, E., Hernández Abreu, Domingo
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
Descripción
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.