SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Composition methods based on an almost symmetric Strang splitting

A. Ostermann and L. Einkemmer

Abstract
Compared to standard integrators, splitting methods often have superior geometric properties. Moreover, high-order schemes can easily be obtained by composition of Strang splitting, whenever the exact partial flows (or semi-flows) are employed. In certain applications, however, only numerical approximations to these flows are available. This is particularly true for many non-linear problems. In such a situation, Strang splitting looses symmetry, and consequently the related composition schemes exhibit severe order reductions.
In this talk, it will be shown how high order composition schemes can be recovered. The procedure is illustrated with typical examples from ordinary and time dependent partial differential equations that arise in applications. This talk is based on the recent paper [1].

Bibliography
[1] L. Einkemmer and A. Ostermann, An almost symmetric Strang splitting scheme for the construction of high order composition methods, arXive preprint, arXiv:1306.1169, 2013.

Organized by         Universidad de Valladolid     IMUVA