Efficient SSP low-storage Runge-Kutta methods
Fecha
2019Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión enviada / Bidali den bertsioa
Identificador del proyecto
ES/1PE/MTM2016-77735
Impacto
|
10.1016/j.cam.2019.112500
Resumen
In this paper we study the efficiency of Strong Stability Preserving (SSP) Runge-Kutta methods that can be implemented with a low number of registers using their Shu-Osher representation. SSP methods have been studied in the literature and stepsize restrictions that ensure numerical monotonicity have been found. However, for some problems, the observed stepsize restrictions are larger than the ...
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In this paper we study the efficiency of Strong Stability Preserving (SSP) Runge-Kutta methods that can be implemented with a low number of registers using their Shu-Osher representation. SSP methods have been studied in the literature and stepsize restrictions that ensure numerical monotonicity have been found. However, for some problems, the observed stepsize restrictions are larger than the theoretical ones. Aiming at obtaining additional properties of the schemes that may explain their efficiency, in this paper we study the influence of the local error term in the observed stepsize restrictions. For this purpose, we consider the family of 5-stage third order SSP explicit
Runge-Kutta methods, namely SSP(5,3), and the Buckley-Leverett equation. We deal with optimal SSP(5,3) schemes whose implementation requires at least 3 memory registers, and non-optimal 2-register SSP(5,3) schemes. The numerical experiments done show that small error constants improve the efficiency of the method in the sense that larger observed SSP coefficients are obtained. [--]
Materias
Runge-Kutta,
Strong stability preserving,
SSP,
Monotonicity,
Total variation diminishing,
TVD,
Low storage,
Local error term,
Initial value problem
Notas
Esta es la versión no revisada del artículo: I. Higueras and T. Roldán, Efficient SSP low-storage Runge–Kutta methods, Journal of Computational and Applied Mathematics
(2019) 112500. Se puede consultar la versión publicada en https://doi.org/10.1016/j.cam.2019.112500.
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila
Entidades Financiadoras
This work was partially supported by the Spanish Research Grant MTM2016-77735-C3-2-P