Locally exact modifications of discrete gradient schemes

TL;DR

This paper introduces energy-preserving, locally exact discrete gradient schemes for multidimensional Hamiltonian systems, enhancing classical methods by ensuring linearization preservation at every point.

Contribution

It develops a novel class of energy-preserving, locally exact modifications of discrete gradient schemes applicable to any discrete gradient in multidimensional Hamiltonian systems.

Findings

Constructed energy-preserving locally exact schemes for Hamiltonian systems.

Applicable modifications found for any discrete gradient.

Enhanced stability and accuracy of numerical integration methods.

Abstract

Locally exact integrators preserve linearization of the original system at every point. We construct energy-preserving locally exact discrete gradient schemes for arbitrary multidimensional canonical Hamiltonian systems by modifying classical discrete gradient schemes. Modifications of this kind are found for any discrete gradient.