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Conversion methods for improving structural analysis of differential-algebraic equation systems

Tan, Guangning, Nedialkov, Nedialko and Pryce, John D. 2017. Conversion methods for improving structural analysis of differential-algebraic equation systems. BIT Numerical Mathematics 57 (3) , pp. 845-865. 10.1007/s10543-017-0655-z

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Abstract

Differential-algebraic equation systems (DAEs) are generated routinely by simulation and modeling environments. Before a simulation starts and a numerical method is applied, some kind of structural analysis (SA) is used to determine which equations to be differentiated, and how many times. Both Pantelides's algorithm and Pryce's Σ-method are equivalent: if one of them finds correct structural information, the other does also. Nonsingularity of the Jacobian produced by SA indicates a success, which occurs on many problems of interest. However, these methods can fail on simple, solvable DAEs and give incorrect structural information including the index. This article investigates Σ-method's failures and presents two conversion methods for fixing them. Both methods convert a DAE on which the Σ-method fails to an equivalent problem on which this SA is more likely to succeed.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Springer Verlag
ISSN: 0006-3835
Date of First Compliant Deposit: 7 July 2017
Date of Acceptance: 30 March 2017
Last Modified: 13 Oct 2017 03:28
URI: http://orca.cf.ac.uk/id/eprint/97749

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