Difference schemes with point symmetries and their numerical tests

Details Difference schemes with point symmetries and their numerical tests Difference schemes with point symmetries and their numerical tests

2006-02-24

arxiv.org/abs/math-ph/0602057v1

Physics

Mathematical Physics

26 pages 7 figures

Scientific paper

10.1088/0305-4470/39/22/006

Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new difference schemes are tested as numerical methods. The obtained numerical solutions are shown to be much more accurate than those obtained by standard methods without an increase in cost. For an example involving a solution with a singularity in the integration region the symmetry preserving scheme, contrary to standard ones, provides solutions valid beyond the singular point.

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