Avoiding the order reduction when solving second-order in time PDEs with Fractional Step Runge–Kutta–Nyström methods

We study some of the main features of Fractional Step Runge–Kutta–Nyström methods when they are used to integrate Initial–Boundary Value Problems of second order in time, in combination with a suitable spatial discretization. We focus our attention on the order reduction phenomenon, which appears if...

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Detalles Bibliográficos
Autores: Moreta, M. Jesús, Bujanda Cirauqui, Blanca, Jorge Ulecia, Juan Carlos
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2016
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/38166
Acceso en línea:https://hdl.handle.net/2454/38166
Access Level:acceso abierto
Palabra clave:Fractional Step Runge–Kutta–Nyström methods
Second-order partial differential equations
Order reduction
Stability
Consistency
Descripción
Sumario:We study some of the main features of Fractional Step Runge–Kutta–Nyström methods when they are used to integrate Initial–Boundary Value Problems of second order in time, in combination with a suitable spatial discretization. We focus our attention on the order reduction phenomenon, which appears if classical boundary conditions are taken at the internal stages. This drawback is specially hard when time dependent boundary conditions are considered. In this paper we present an efficient technique, very simple and computationally cheap, which allows us to avoid the order reduction; such technique consists in modifying the boundary conditions for the internal stages of the method.