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On Decomposition of Algebraic PDE Systems into Simple Subsystems

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Abstract

In this paper we present an algorithmization of the Thomas method for splitting a system of partial differential equations and (possibly) inequalities into triangular subsystems whose Thomas called simple. The splitting algorithm is applicable to systems whose elements are differential polynomials in unknown functions and polynomials in independent variables. Simplicity properties of the subsystems make easier their completion to involution. Our algorithmization uses algebraic Gröbner bases to avoid some unnecessary splittings.

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Authors and Affiliations

  1. Joint Institute for Nuclear Research, 141980, Dubna, Russia

    Vladimir P. Gerdt

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  1. Vladimir P. Gerdt
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Correspondence to Vladimir P. Gerdt.

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This research was partially supported by grant 07-01-00660 from the Russian Foundation for Basic Research.

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Gerdt, V.P. On Decomposition of Algebraic PDE Systems into Simple Subsystems. Acta Appl Math 101, 39–51 (2008). https://doi.org/10.1007/s10440-008-9202-x

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  • DOI: https://doi.org/10.1007/s10440-008-9202-x

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