Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests

摘要: The main purpose of this article is to show how structure reected in partial dierential equations can be preserved a discrete world and dierence schemes. Three dierent preserving discretizations the Liouville equation are presented then used solve specic boundary value problems. results compared with exact solutions satisfying same conditions. All three on four point lattices. One preserves linearizability equation, another innite dimensional symmetry group as higher symmetries, third maximal nite subgroup symmetries. A 9-point invariant scheme that gives better approximation but worse numerical for discussed.