Index reduction of differential algebraic equations by differential Dixon resultant

Index reduction of differential algebraic equations by differential Dixon resultant High index differential algebraic equations (DAEs) are ordinary differential equations (ODEs) with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields. In this paper, we generalize the idea of differential elimination with Dixon resultant to polynomially nonlinear DAEs. We propose a new algorithm for index reduction of DAEs and establish the notion of differential Dixon resultant, which can provide the differential resultant of the enlarged system of original equations. To make use of structure of DAEs, variable pencil technique is given to determine the termination of differentiation. Moreover, we also provide a heuristic method for removing the extraneous factors from differential resultant. The experimentation shows that the proposed algorithm outperforms existing ones for many examples taken from the literature. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

Index reduction of differential algebraic equations by differential Dixon resultant

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Inc.
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2017.12.029
Publisher site
See Article on Publisher Site

Abstract

High index differential algebraic equations (DAEs) are ordinary differential equations (ODEs) with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields. In this paper, we generalize the idea of differential elimination with Dixon resultant to polynomially nonlinear DAEs. We propose a new algorithm for index reduction of DAEs and establish the notion of differential Dixon resultant, which can provide the differential resultant of the enlarged system of original equations. To make use of structure of DAEs, variable pencil technique is given to determine the termination of differentiation. Moreover, we also provide a heuristic method for removing the extraneous factors from differential resultant. The experimentation shows that the proposed algorithm outperforms existing ones for many examples taken from the literature.

Journal

Applied Mathematics and ComputationElsevier

Published: Jul 1, 2018

References

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