Composition Methods for Dynamical Systems Separable into Three Parts

TL;DR

This paper introduces new fourth-order composition methods for numerically solving initial value problems in differential equations, optimized for problems separable into three explicitly solvable parts, and demonstrates their improved performance.

Contribution

It proposes novel fourth-order splitting methods tailored for three-part separable problems, preserving geometric properties and outperforming existing methods.

Findings

Methods show improved accuracy over previous splitting techniques.

Numerical examples confirm enhanced performance.

Geometric property preservation is achieved by design.

Abstract

New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a way that each part is explicitly solvable. The methods are obtained by applying different optimization criteria and preserve geometric properties of the continuous problem by construction. Different numerical examples exhibit their improved performance with respect to previous splitting methods in the literature.