Splitting methods with complex coefficients.

link: http://arxiv.org/abs/1001.1549
Abstract

Splitting methods for the numerical integration of differential equations of
order greater than two involve necessarily negative coefficients. This order
barrier can be overcome by considering complex coefficients with positive real
part. In this work we review the composition technique used to construct
methods of this class, propose new sixth-order integrators and analyze their
main features on a pair of numerical examples, in particular how the errors are
propagated along the evolution.