FRONTIERS IN COMPUTATIONAL ASTROPHYSICS

Particle and Flames in Radiative and Magnetic Flows

October 11-15, 2010
Lyon, France

Contribution of Assyr Abdulle

Title

Explicit methods for deterministic and stochastic differential equations with multiple scales

Topics

"Stellar structure and evolution""Explosive fate of stars""Planetary atmospheric circulation"

Keywords

Ordinary and stochastic differential equations, stiff and multiscale problems, stabilized methods, explicit methods, Runge-Kutta methods

Abstract

Numerous methods have been recently developed for (ordinary, partial or stochastic) differential equations with multiple scales. A successful approach for stiff time dependent differential equations relies on the use of implicit solvers to damp the fast scales present in the problems. This comes at the cost of solving (possibly large and badly conditioned) linear systems. However, for classes of (dissipative) stiff problems, explicit stabilized methods can be very efficient. We will present such methods and discuss their recent extension to stochastic differential equations. Example and applications will also be discussed.