The self-adjoint 5-point and 7-point difference operators, the associated Dirichlet problems, Darboux transformations and Lelieuvre formulas

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We present some basic properties of two distinguished discretizations of elliptic operators: the self-adjoint 5-point and 7-point schemes on a two dimensional lattice. We first show that they allow to solve Dirichlet boundary value problems; then we present their Darboux transformations. Finally we construct their Lelieuvre formulas and we show that, at the level of the normal vector and in full analogy with their continuous counterparts, the self-adjoint 5-point scheme characterizes a two dimensional quadrilateral lattice (a lattice whose elementary quadrilaterals are planar), while the self-adjoint 7-point scheme characterizes a generic 2D lattice.
20 pages, 6 figures, submitted to Glasgow Mathematical Journal Trust for Island II proceedinds

Keywords

Exactly Solvable and Integrable Systems

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/80671

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0402038
 http://arxiv.org/abs/nlin/0402038

Collections

arXiv