Construction of additive semi-implicit Runge-Kutta methods with low-storage requirements
Fecha
2016Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Impacto
|
10.1007/s10915-015-0116-2
Resumen
Space discretization of some time-dependent partial differential equations gives rise to systems of
ordinary differential equations in additive form whose terms have different stiffness properties. In these
cases, implicit methods should be used to integrate the stiff terms while efficient explicit methods can be
used for the non-stiff part of the problem. However, for systems with a large num ...
[++]
Space discretization of some time-dependent partial differential equations gives rise to systems of
ordinary differential equations in additive form whose terms have different stiffness properties. In these
cases, implicit methods should be used to integrate the stiff terms while efficient explicit methods can be
used for the non-stiff part of the problem. However, for systems with a large number of equations, memory
storage requirement is also an important issue. When the high dimension of the problem compromises
the computer memory capacity, it is important to incorporate low memory usage to some other properties of the scheme.
In this paper we consider Additive Semi-Implicit Runge-Kutta (ASIRK) methods, a class of implicitexplicit
Runge-Kutta methods for additive differential systems. We construct two second order 3-stage
ASIRK schemes with low-storage requirements. Having in mind problems with stiffness parameters,
besides accuracy and stability properties, we also impose stiff accuracy conditions. The numerical experiments done show the advantages of the new methods. [--]
Materias
Additive Runge-Kutta methods,
Strong stability preserving,
Low-storage,
Stiff problems,
Time discretization schemes
Editor
Springer US
Publicado en
Journal of Scientific Computing (2016) 67:1019–1042
Notas
The final publication is available at Springer via
http://dx.doi.org/ 10.1007/s10915-015-0116-2
Departamento
Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática /
Nafarroako Unibertsitate Publikoa. Matematika eta Informatika Ingeniaritza Saila
Versión del editor
Entidades Financiadoras
Supported by Ministerio de Economía y Competividad, project MTM2011-23203.