A new look at dummy derivatives for differential-algebraic equations

Pryce, John D. ORCID: https://orcid.org/0000-0003-1702-7624 and McKenzie, Ross 2016. A new look at dummy derivatives for differential-algebraic equations. Belair, J., Frigaard, I. A., Kunze, H., Makarov, R., Melnik, R. and Spiteri, R. J., eds. Mathematical and Computational Approaches in Advancing Modern Science and Engineering, Springer International Publishing, pp. 713-723. (10.1007/978-3-319-30379-6_64)

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Abstract

We show the dummy derivatives index reduction method for DAEs, introduced in 1993 by Mattsson & Söderlind, is a particular case of the Pryce ΣΣ-method solution scheme. We give a pictorial display of the underlying block triangular form. This approach gives a simple general method to cast the reduced system in semi-explicit index 1 form, combining order reduction and index reduction in one process. It also shows each DD scheme for a given DAE is uniquely described by an integer “DDspec” vector δδ. The method is illustrated by an example. We give various reasons why, contrary to common belief, converting further from semi-explicit index 1 form to an explicit ODE, can be a good idea for numerical solution.

Item Type:	Book Section
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer International Publishing
ISBN:	9783319303796
Date of First Compliant Deposit:	25 January 2017
Date of Acceptance:	10 November 2016
Last Modified:	02 Nov 2022 10:11
URI:	https://orca.cardiff.ac.uk/id/eprint/97751

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