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Consistency Analysis of Finite Difference Approximations to PDE Systems

  • Vladimir P. Gerdt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7125)

Abstract

We consider finite difference approximations to systems of polynomially-nonlinear partial differential equations the coefficients of which are rational functions over rationals in the independent variables. The notion of strong consistency which we introduced earlier for linear systems is extended to nonlinear ones. For orthogonal and uniform grids we describe an algorithmic procedure for the verification of the strong consistency based on the computation of difference standard bases. The concepts and algorithmic methods of the present paper are illustrated by two finite difference approximations to the two-dimensional Navier-Stokes equations. One of these approximations is strongly consistent, while the other is not.

Keywords

systems of partial differential equations involution Thomas decomposition finite difference approximations consistency difference standard bases Navier-Stokes equations computer algebra 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Vladimir P. Gerdt
    • 1
  1. 1.Laboratory of Information TechnologiesJoint Institute for Nuclear ResearchDubnaRussia

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