Invariant difference schemes and their application to $SL(2,\mathbb{R})$ invariant ordinary differential equations

Details Invariant difference schemes and their application to $SL(2,\mathbb{R})$ invariant ordinary differential equations Invariant difference schemes and their application to $SL(2,\mathbb{R})$ invariant ordinary differential equations

2009-06-16

arxiv.org/abs/0906.2980v2

Physics

Mathematical Physics

11 pages, 4 figures. Title, abstract, introduction and conclusion were rewritten for a better presentation and understanding o

Scientific paper

10.1088/1751-8113/42/45/454016

We present an exposition of a method of discretizing ordinary differential equations while preserving their Lie point symmetries. This method is very general and can be applied to any ODE with a nontrivial symmetry group. The method is applied to obtain numerical slutions of second and third order ODEs invariant under two different realizations of $SL(2,\mathbb{R})$. The symmetry preserving method is shown to provide a better qualitative description of solutions than standard methods. In particular it provides solutions that are valid close to singularities and beyond them.

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