The integration of systems of linear PDEs using conservation laws of syzygies
type: Item
instance of: scholarly article
title: The integration of systems of linear PDEs using conservation laws of syzygies
zbMATH Open document ID: 1026.35003
DOI: 10.1016/S0747-7171(03)00020-8
author: D. Massart
published in: Journal of Symbolic Computation
publication date: 2003-08-21T00:00:00Z
review text: A new integration technique is presented for systems of linear partial differential equations for which syzygies can be formulated that obey conservation laws. These syzygies come for free as a by-product of the differential Gröbner basis computation. Compared with the more obvious way of integrating a single equation and substituting the result in other equations the new technique integrates more than one equation simultaneously and therefore introduce temporarily fewer new functions of integration that in addition depend on fewer variables. Especially for high order PDE systems in many variables the conventional integration technique may lead to an explosion of the number of functions of integration which is avoided with the new method. A future benefit is that redundant free functions in the solution are either prevented or that their number is at least reduced.
Mathematics Subject Classification ID: 35A25
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 35N10
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 1968934
zbMATH Keywords: differential Gröbner basis computation
reviewed by: Valeriy Yumaguzhin
describes a project that uses: diffgrob2
MaRDI profile type: Publication
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full work available at URL: s0747-7171(03)00020-8
OpenAlex ID: W2047164313
description: scientific article; zbMATH DE number 1968934