Georg Jansing

Georg Jansing, Achim Schädle

Convergence of a triple splitting method originally proposed by T. Tückmantel,et.al. [IEEE Transactions on Plasma Science, 38(9):2383--2389, 2010] for the solution of a simple Vlasov-Maxwell system, that describes laser plasma interactions with overdense plasmas, is analyzed. For classical explicit integrators it is the large density parameter that would impose a restriction on the time step size to make the integration stable. The triple splitting method contains an exponential integrator in its central component and was specifically designed for systems that describe laser plasma interactions and overcomes this restriction. We rigorously analyze a slightly generalized version of the original method. This analysis enables us to identify modifications of the original scheme, such that a second order convergent scheme is obtained.

Georg Jansing

EXPODE is a MATLAB toolbox for exponential time integration. It supports exponential Runge-Kutta- and Rosenbrock-methods, linearized and non-linearized multistep-methods and the EXP4. We support evaluation of the arising matrix functions either directly or by a Krylov method. We also have adaptive step width control for some of the methods. This document contains the documentation of the software package. The software itself is available from http://www.am.uni-duesseldorf.de/en/Research/03_Software.php .