How AD can help solve differential-algebraic equations

Pryce, John ORCID: https://orcid.org/0000-0003-1702-7624, Nedialkov, Nedialko S., Tan, Guangning and Li, Xiao 2018. How AD can help solve differential-algebraic equations. Optimization Methods and Software 10.1080/10556788.2018.1428605

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Abstract

A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of the so-called index reduction or regularization, to prepare them for numerical solution. This is often done with the help of a computer algebra system. We show in two significant cases that it can be done efficiently by pure algorithmic differentiation. The first is the Dummy Derivatives method; here we give a mainly theoretical description, with tutorial examples. The second is the solution of a mechanical system directly from its Lagrangian formulation. Here, we outline the theory and show several non-trivial examples of using the ‘Lagrangian facility’ of the Nedialkov– Pryce initial-value solver DAETS, namely a spring-mass-multi-pendulum system; a prescribed-trajectory control problem; and long-time integration of a model of the outer planets of the solar system, taken from the DETEST testing package for ODE solvers.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Publisher:	Taylor and Francis
ISSN:	1055-6788
Funders:	Leverhulme Trust; NSERC Canada
Date of First Compliant Deposit:	28 March 2018
Date of Acceptance:	10 January 2018
Last Modified:	27 Nov 2024 13:15
URI:	https://orca.cardiff.ac.uk/id/eprint/110289

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