Discretization of partial differential equations preserving their physical symmetries
Valiquette, Francis ; Winternitz, Pavel
arXiv, 0507061 / Harvested from arXiv
Text on arXiv
A procedure for obtaining a "minimal" discretization of a partial differential equation, preserving all of its Lie point symmetries is presented. "Minimal" in this case means that the differential equation is replaced by a partial difference scheme involving N difference equations, where N is the number of independent and dependent variable. We restrict to one scalar function of two independent variables. As examples, invariant discretizations of the heat, Burgers and Korteweg-de Vries equations are presented. Some exact solutions of the discrete schemes are obtained.
Publié le : 2005-07-24
Classification:  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  39A99,  58D19 
@article{0507061,
     author = {Valiquette, Francis and Winternitz, Pavel},
     title = {Discretization of partial differential equations preserving their
  physical symmetries},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0507061}
}

Valiquette, Francis; Winternitz, Pavel. Discretization of partial differential equations preserving their
  physical symmetries. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0507061/