Acta Applicandae Mathematicae

, Volume 101, Issue 1–3, pp 39–51 | Cite as

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.

Keywords

PDEs Completion to involution Algebraically simple system Decomposition algorithm Thomas splitting method Gröbner basis 
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© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Joint Institute for Nuclear ResearchDubnaRussia

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