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: | 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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