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

Invited Talk

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On some splitting methods involving high order derivatives

F. Casas

Abstract
In this talk we review some splitting schemes for Hamiltonian systems of the form $H(q,p) = T(p) + V(q)$, with $T(p)$ quadratic in momenta, which involve the flow associated with the bracket $[V,[T,V]]$ alongside the potential $V(q)$. In this way second order derivatives of the potential have to be computed at each step along the integration interval. Some new methods involving even higher order derivatives of the potential are considered. Methods within this class require less stages than standard splitting schemes to achieve high order of accuracy. We analyze the applicability of the new methods to specific problems where the evaluation of the nested brackets is not particularly costly.

Organized by         Universidad de Valladolid     IMUVA