Exponential Runge–Kutta Methods for Stiff Kinetic Equations

Exponential Runge-Kutta Methods for Stiff Kinetic Equations

Abstract. We introduce a class of exponential Runge-Kutta integration methods for kinetic equations. The methods are based on a decomposition of the collision operator into an equilibrium and a non equilibrium part and are exact for relaxation operators of BGK type. For Boltzmann type kinetic equations they work uniformly for a wide range of relaxation times and avoid the solution of nonlinear ...

Explicit methods for stiff stochastic differential equations

Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-square stable) stiff stochastic differential equations. Standard explicit methods, as for example the EulerMaruyama method, face severe stepsize...

Two-Parameter, Arbitrary Order, Exponential Approximations for Stiff Equations

A two-parameter family of approximations to the exponential function is considered. Constraints on the parameters are determined which guarantee the approximations are ^-acceptable. The suitability of these approximations for 2-point vl-stable exponential fitting is established. Several numerical methods, which produce these approximations when solving y = \v, are presented.

Scalable Methods for Kinetic Equations

Scalable Methods for Kinetic Equations