Martina L. Structure-preserving discretizations of the Liouville equation, talk at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic (abstract)
Speaker: Luigi Martina
Title: Structure-preserving discretizations of the Liouville equation
Abstract:
Symmetry structures of partial differential equations can be reflected in difference schemes. In particular, the Liouville equation is a prototype of systems in which three different structure-preserving discretizations on four point lattices can be presented and, then, used to solve specific boundary value problems. The results are compared with exact solutions satisfying the same boundary conditions. One preserves linearizability of the equation, another the infinite-dimensional symmetry group as higher symmetries, the third preserves the maximal finite-dimensional subgroup of the symmetry group as point symmetries. A 9-point invariant scheme is also considered, but worse numerical solutions are presented and discussed.