Compositions of pseudo-symmetric integrators with complex coefficients for the numerical integration of differential equations

TL;DR

This paper introduces a new class of symmetric and symplectic integrators created through double jump compositions with complex coefficients, offering higher order accuracy and efficiency for differential equation numerical solutions.

Contribution

It presents a novel composition technique using complex coefficients and projections, achieving high-order symmetry and symplecticity with fewer stages than traditional methods.

Findings

Integrators are symmetric and symplectic up to high orders.

Fewer stages needed compared to standard compositions.

Expected to produce faster numerical methods.

Abstract

In this paper, we are concerned with the construction and analysis of a new class of methods obtained as double jump compositions with complex coefficients and projection on the real axis. It is shown in particular that the new integrators are symmetric and symplectic up to high orders if one uses a symmetric and symplectic basic method. In terms of efficiency, the aforementioned technique requires fewer stages than standard compositions of the same orders and is thus expected to lead to faster methods.