On alternating-conjugate splitting methods
Abstract
The new class of alternating-conjugate splitting methods is presented and analyzed. They are obtained by concatenating a given composition involving complex coefficients with the same composition but with the complex conjugate coefficients. We show that schemes of this type exhibit a good long time behavior when applied to linear unitary and linear Hamiltonian systems, in contrast with other methods based on complex coefficients, and study in detail their preservation properties. We also present new schemes within this class up to order 6 that exhibit a better efficiency than state-of-the-art splitting methods with real coefficients for some classes of problems.
Cite
@article{arxiv.2503.08453,
title = {On alternating-conjugate splitting methods},
author = {J. Bernier and S. Blanes and F. Casas and A. Escorihuela-Tomàs},
journal= {arXiv preprint arXiv:2503.08453},
year = {2025}
}
Comments
This paper has been accepted for publication in Mathematics of Computation in its current version