Asymptotic Preserving and Multiscale Methods for Kinetic and Hyperbolic Problems

HIGH ORDER SEMI-IMPLICIT SCHEMES FOR KINETIC EQUATIONS

Francis Filbet

Paul Sabatier University, Toulouse III
[SLIDES]

We consider a new formulation of implicit-explicit (IMEX) Runge-Kutta (R-K) methods for the numerical discretization of time dependent partial differential equations. The approach is based on identifying the (linear) dependence on the unknown of the system which generates the stiffness. Only the stiff dependence is treated implicitly, then making the whole method much simpler than fully implicit ones. This approach generalizes classical IMEX methods based on additive and partitioned R-K, and allows a novel application of semi-implicit schemes. We adopt several semi- implicit R-K methods up to order three. We illustrate the effectiveness of the new approach with many applications to reaction-diffusion, convection diffusion and nonlinear diffusion system of equations.