Positivity-preserving and entropy-decaying IMEX methods
-
Autores: Teodoro Roldán Marrodán, Inmaculada Higueras Sanz
- Localización: Ninth international conference Zaragoza-Pau on applied mathematics and statistics: Jaca (Spain). September 19-21, 2005 / coord. por Monique Madaune-Tort , 2006, ISBN 84-7733-871-X, págs. 129-136
- Idioma: inglés
- Enlaces
-
Resumen
Ordinary differential equations containing additive terms with different stiffness properties may arise when some time dependent partial differential equations are discretized in space. IMEX Runge-Kutta methods are suitable to treat this kind of problems.
Sometimes the solutions to these problems have qualitative properties (norm, energy, entropy, total variation, positivity, etc) that represent important physical features of the problem. In this case, in order to preserve the physical meaning of the numerical solution, it is important to maintain these properties with both the spatial discretization and the time stepping method. IMEX Runge-Kutta methods methods can preserve some qualitative properties of the exact solution under certain stepsize restrictions. In this paper we review some results concerned to these preserving properties and show how they can be used for some problems
