On symmetric-conjugate composition methods in the numerical integration of differential equations
Numerical Analysis
2021-01-12 v1 Numerical Analysis
Abstract
We analyze composition methods with complex coefficients exhibiting the so-called ``symmetry-conjugate'' pattern in their distribution. In particular, we study their behavior with respect to preservation of qualitative properties when projected on the real axis and we compare them with the usual left-right palindromic compositions. New schemes within this family up to order 8 are proposed and their efficiency is tested on several examples. Our analysis shows that higher-order schemes are more efficient even when time step sizes are relatively large.
Keywords
Cite
@article{arxiv.2101.04100,
title = {On symmetric-conjugate composition methods in the numerical integration of differential equations},
author = {Sergio Blanes and Fernando Casas and Philippe Chartier and Alejandro Escorihuela-Tomàs},
journal= {arXiv preprint arXiv:2101.04100},
year = {2021}
}
Comments
24 pages, 4 figures