High order semi-implicit schemes for time dependent partial differential equations
Résumé
In this paper we consider a new formulation of implicit-explicit (IMEX) methods for the numerical discretization of time dependent partial differential equations. We construct several semi- implicit Runge-Kutta methods up to order three. This approach is particularly suited for problems where the stiff and non-stiff components cannot be well separated. We present different numerical simulations for reaction-diffusion, convection diffusion and nonlinear diffusion system of equations. Finally, we conclude by a stability analysis of the schemes for linear problems.
Domaines
Analyse numérique [math.NA]
Origine : Fichiers produits par l'(les) auteur(s)