Symmetry preserving discretization of 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.

12 pages, 3 figures, submitted to Journal of Nonlinear Mathematical Physics

References in corpus (4)

• Continuous Symmetries of Difference Equations
• Lie point symmetries of difference equations and lattices
• Difference schemes with point symmetries and their numerical tests
• Lie Symmetries and Exact Solutions of First Order Difference Schemes

Cited by in corpus (6)

• On the integrability of a new lattice equation found by multiple scale analysis
• Invariant difference schemes and their application to $SL(2,\mathbb{R})$ invariant ordinary differential equations
• Lie-point symmetries of the discrete Liouville equation
• The Korteweg-de Vries equation and its symmetry-preserving discretization
• Invariant finite-difference schemes with conservation laws preservation for one-dimensional MHD equations
• Invariant Discretization of Partial Differential Equations Admitting Infinite-Dimensional Symmetry Groups