In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this paper, we design numerical methods for a PDE system arising in… (More)
Lie-symmetry based integrators are constructed in order to preserve the local invariance properties of the equations. The geometrical methods leading to discretized equations for numerical computations involve many different concepts. Therefore they give rise to numerical schemes that vary in the accuracy, in the computational cost and in the… (More)
A Mathematica based program has been elaborated in order to determine the symmetry group of a finite difference equation. The package provides functions which enable us to solve the determining equations of the related Lie group.
Differential equations arising in fluid mechanics are usually derived from the intrinsic properties of mechanical systems, in the form of conservation laws, and bear symmetries, which are not generally preserved by a finite difference approximation , and leading to inaccurate numerical results. This paper proposes a method that enables us to build a scheme… (More)