Order barrier for low-storage DIRK methods with positive weights

In this paper we study an order barrier for low-storage diagonally implicit Runge-Kutta (DIRK) methods with positive weights. The Butcher matrix for these schemes, that can be implemented with only two memory registers in the van der Houwen implementation, has a special structure that restricts the...

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Detalles Bibliográficos
Autores: Higueras Sanz, Inmaculada, Roldán Marrodán, Teodoro
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
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:2454/34791
Acceso en línea:https://hdl.handle.net/2454/34791
Access Level:acceso abierto
Palabra clave:Diagonally Implicit
DIRK
Runge-Kutta
Low-storage
Symplectic
Stiff problems
Time discretization
Composition
Descripción
Sumario:In this paper we study an order barrier for low-storage diagonally implicit Runge-Kutta (DIRK) methods with positive weights. The Butcher matrix for these schemes, that can be implemented with only two memory registers in the van der Houwen implementation, has a special structure that restricts the number of free parameters of the method. We prove that third order low-storage DIRK methods must contain negative weights, obtaining the order barrier p ≤ 2 for these schemes. This result extends the well known one for symplectic DIRK methods, which are a particular case of low-storage DIRK methods. Some other properties of second order low-storage DIRK methods are given.