Structural analysis based dummy derivative selection for differential algebraic equations

McKenzie, Ross and Pryce, John D. ORCID: https://orcid.org/0000-0003-1702-7624 2017. Structural analysis based dummy derivative selection for differential algebraic equations. BIT Numerical Mathematics 57 (2) , pp. 433-462. 10.1007/s10543-016-0642-9

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Abstract

The signature matrix structural analysis method developed by Pryce provides more structural information than the commonly used Pantelides method and applies to differential-algebraic equations (DAEs) of arbitrary order. It is useful to consider how existing methods using the Pantelides algorithm can benefit from such structural analysis. The dummy derivative method is a technique commonly used to solve DAEs that can benefit from such exploitation of underlying DAE structures and information found in the Signature Matrix method. This paper gives a technique to find structurally necessary dummy derivatives and how to use different block triangular forms effectively when performing the dummy derivative method and then provides a brief complexity analysis of the proposed approach. We finish by outlining an approach that can simplify the task of dummy pivoting.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Uncontrolled Keywords:	DAEs Numerical Analysis
Additional Information:	This article is distributed under the terms of the Creative Commons Attribution 4.0 International License
Publisher:	Springer Verlag
ISSN:	0006-3835
Funders:	The Leverhulme Trust
Date of First Compliant Deposit:	30 May 2017
Date of Acceptance:	8 November 2016
Last Modified:	05 May 2023 12:50
URI:	https://orca.cardiff.ac.uk/id/eprint/100978

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