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Index reduction of differential algebraic equations by differential algebraic elimination | | Xiaolin Qin
; Lu Yang
; Yong Feng
; Bernhard Bachmann
; Peter Fritzson
; | | Date: |
20 Apr 2015 | | 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 algebraic elimination, which can
provide the differential algebraic 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
heuristics method for removing the extraneous factors from differential
algebraic resultant. The experimentation shows that the proposed algorithm
outperforms existing ones for many examples taken from the literature. | | Source: | arXiv, 1504.4977 | | Services: | Forum | Review | PDF | Favorites | |
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