Lie groups and numerical solutions of differential equations: Invariant\n discretization versus differential approximation

2013/04/25 by D. Levi, P. Winternitz, Levi, Decio +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1304.7016

openalex publication_date 2013/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We briefly review two different methods of applying Lie group theory in the\nnumerical solution of ordinary differential equations. On specific examples we\nshow how the symmetry preserving discretization provides difference schemes for\nwhich the "first differential approximation" is invariant under the same Lie\ngroup as the original ordinary differential equation.\n

Related

• Notes on Lie symmetry group methods for differential equations
• Approximate Lie Group Analysis of Finite-difference Equations
• Lie group computation of finite difference schemes
• Lie Transformation Groups -- An Introduction to Symmetry Group Analysis of Differential Equations
• Ordinary Differential Equations through Dimensional Analysis