High order semi-implicit schemes for time dependent partial differential equations

Sebastiano Boscarino (1) , Francis Filbet (2, 3) , Giovanni Russo (1)

1 Departmement de Mathématiques et Informatique
2 ICJ - Institut Camille Jordan
3 KALiFFE - Kinetic models AppLIed for Future of Fusion Energy

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.

Mots clés: time discretization; stiff ode; pde

Domaines: Analyse numérique [math.NA]

Sebastiano Boscarino, Francis Filbet, Giovanni Russo. High order semi-implicit schemes for time dependent partial differential equations. 2014. ⟨hal-00983924v2⟩