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Dimension Polynomials and the Einstein’s Strength of Some Systems of Quasi-linear Algebraic Difference Equations

Abstract

In this paper we present a method of characteristic sets for inversive difference polynomials and apply it to the analysis of systems of quasi-linear algebraic difference equations. We describe characteristic sets and compute difference dimension polynomials associated with some such systems. Then we apply our results to the comparative analysis of difference schemes for some PDEs from the point of view of their Einstein’s strength. In particular, we determine the Einstein’s strength of standard finite-difference schemes for the Murray, Burgers and some other reaction–diffusion equations.

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Correspondence to Alexander Levin.

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This work was completed with the support of the NSF Grant CCF-1714425.

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Evgrafov, A., Levin, A. Dimension Polynomials and the Einstein’s Strength of Some Systems of Quasi-linear Algebraic Difference Equations. Math.Comput.Sci. (2020) doi:10.1007/s11786-019-00430-7

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Keywords

  • Difference polynomial
  • Autoreduced set
  • Characteristic set
  • Einstein’s strength
  • Difference scheme

Mathematics Subject Classification

  • Primary 12H05
  • Secondary 12H10
  • 39A05
  • 35K57