Preserving first integrals with symmetric Lie group methods

TL;DR

This paper introduces a generalized discrete gradient approach to develop numerical methods that preserve first integrals for differential equations on Lie groups, enhancing the accuracy and stability of simulations involving geometric structures.

Contribution

It extends the discrete gradient method to Lie groups, enabling the preservation of first integrals in geometric numerical integration.

Findings

Methods successfully preserve first integrals in Lie group differential equations

Enhanced stability and accuracy demonstrated in numerical experiments

Applicable to a broad class of geometric problems involving Lie groups

Abstract

The discrete gradient approach is generalized to yield integral preserving methods for differential equations in Lie groups.