Invariant discretization of partial differential equations admitting infinite-dimensional symmetry groups |
| |
Authors: | Raphaël Rebelo Francis Valiquette |
| |
Institution: | 1. Centre de Recherche Mathématiques, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, QC, Canada H3C 3J7raph.rebelo@gmail.com;3. Department of Mathematics, SUNY at New Paltz, New Paltz, NY 12561, USA |
| |
Abstract: | This paper is concerned with the invariant discretization of differential equations admitting infinite-dimensional symmetry groups. By way of example, we first show that there are differential equations with infinite-dimensional symmetry groups that do not admit enough joint invariants preventing the construction of invariant finite difference approximations. To solve this shortage of joint invariants we propose to discretize the pseudo-group action. Computer simulations indicate that the numerical schemes constructed from the joint invariants of discretized pseudo-group can produce better numerical results than standard schemes. |
| |
Keywords: | infinite-dimensional Lie pseudo-groups joint invariants moving frames |
|
|