Splitting methods with complex coefficients

TL;DR

This paper reviews and develops complex-coefficient splitting methods for higher-order differential equations, introducing new sixth-order integrators and analyzing their error propagation through numerical examples.

Contribution

It proposes new sixth-order splitting integrators with complex coefficients and analyzes their properties, overcoming the negative coefficient limitation of traditional methods.

Findings

New sixth-order integrators with complex coefficients

Positive real part coefficients improve stability

Error propagation analyzed through numerical examples

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.