Bård Skaflestad

Exponential integrators for differential equations

History, order analysis and construction

DIFTA 2005–01–03

Abstract: We present a brief historical introduction to exponential integrators for differential equations. A general format for such schemes is introduced and we derive order conditions based on B-series and bicoloured rooted trees. Zennaro's ‘Natural Continuous Extension’ is generalised to enable a relatively easy framework for constructing new schemes. Additionally, we discuss the choice of coefficient functions and give lower bounds on the dimension of the space of coeffcient functions.

If time permits, some new schemes of orders 4 and 5 will be presented as examples of the construction procedure. Numerical results will be presented.