Palindromic 3-stage splitting integrators, a roadmap

TL;DR

This paper explores a family of palindromic three-stage splitting integrators, identifying parameter choices that enhance efficiency and accuracy over traditional methods like Strang/Verlet, with applications in PDEs and molecular dynamics.

Contribution

It introduces a two-parameter family of palindromic three-stage splitting formulas and identifies optimal parameters for improved performance.

Findings

Certain parameter choices outperform Strang/Verlet in efficiency.

One method achieves effective order four for PDE integration.

Perturbations of Strang improve molecular dynamics simulations.

Abstract

The implementation of multi-stage splitting integrators is essentially the same as the implementation of the familiar Strang/Verlet method. Therefore multi-stage formulas may be easily incorporated into software that now uses the Strang/Verlet integrator. We study in detail the two-parameter family of palindromic, three-stage splitting formulas and identify choices of parameters that may outperform the Strang/Verlet method. One of these choices leads to a method of effective order four suitable to integrate in time some partial differential equations. Other choices may be seen as perturbations of the Strang method that increase efficiency in molecular dynamics simulations and in Hybrid Monte Carlo sampling.