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Discretizing the Liouville equation preserving the symmetries


por el

Dr. Decio Levi


Universita Degli Studi Roma Tre, Italy

Resumen:
The main purpose of this seminar is to show how symmetry structures in partial differential equations can be preserved in a discrete world and reflected in difference schemes. Three different structure preserving discretizations of the Liouville equation are presented and then used to solve specific boundary value problems. The results are compared with exact solutions satisfying the same boundary conditions. All three discretizations are on four point lattices. One preserves linearizability of the equation, another the infinite-dimensional symmetry group as higher symmetries, the third one preserves the maximal finite-dimensional subgroup of the symmetry group as point symmetries. A 9-point invariant scheme that gives a better approximation of the equation, but significantly worse numerical results for solutions is presented and discussed.

Miércoles 14 de diciembre, 2016
18:00 hrs.
Salón 203, Edificio Anexo, IIMAS

Informes: coloquiomym@gmail.com, o al 5622-3564.