Index reduction of differential algebraic equations by differential Dixon resultant

Xiaolin Qin, Lu Yang, Yong Feng, Bernhard Bachmann and Peter Fritzson

Applied Mathematics and Computation, 2018, vol. 328, issue C, 189-202

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.

Keywords: Index reduction; Differential Dixon resultant; Differential elimination; Variable pencil; Differential algebraic equations (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:328:y:2018:i:c:p:189-202

DOI: 10.1016/j.amc.2017.12.029

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