Symmetry preserving discretization of SL(2,R) invariant equations

TL;DR

This paper demonstrates that numerical methods which incorporate Lie point symmetries, specifically for SL(2,R) invariant nonlinear ODEs, outperform standard numerical approaches.

Contribution

It introduces symmetry-preserving discretization techniques for SL(2,R) invariant equations, improving numerical solutions by leveraging Lie group symmetries.

Findings

Symmetry-preserving methods yield more accurate solutions.

Incorporating Lie symmetries enhances numerical stability.

Standard methods are less effective for SL(2,R) invariant equations.

Abstract

Nonlinear ODEs invariant under the group SL(2,R) are solved numerically. We show that solution methods incorporating the Lie point symmetries provide better results than standard methods.