Discretization of partial differential equations preserving their physical symmetries

@article{Valiquette2005DiscretizationOP,
  title={Discretization of partial differential equations preserving their physical symmetries},
  author={Francis Valiquette and Pavel Winternitz},
  journal={Journal of Physics A},
  year={2005},
  volume={38},
  pages={9765-9783}
}
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 variables. We restrict ourselves to one scalar function of two independent variables. As examples, invariant discretizations of the heat, Burgers and Korteweg–de… Expand

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