BibTeX
@ARTICLE{
Pryce2018HAc,
crossref = "Christianson2018Sio",
author = "John D. Pryce and Nedialko S. Nedialkov and Guangning Tan and Xiao Li",
title = "How {AD} can help solve differentialalgebraic equations",
journal = "Optimization Methods \& Software",
volume = "33",
number = "46",
pages = "729749",
year = "2018",
publisher = "Taylor \& Francis",
doi = "10.1080/10556788.2018.1428605",
url = "https://doi.org/10.1080/10556788.2018.1428605",
eprint = "https://doi.org/10.1080/10556788.2018.1428605",
abstract = "A characteristic feature of differentialalgebraic equations is that one needs to
find derivatives of some of their equations with respect to time, as part of the socalled 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
nontrivial examples of using the ‘Lagrangian facility’ of the
Nedialkov–Pryce initialvalue solver DAETS, namely a springmassmultipendulum system; a
prescribedtrajectory control problem; and longtime integration of a model of the outer planets of
the solar system, taken from the DETEST testing package for ODE solvers.",
booktitle = "Special issue of Optimization Methods \& Software: Advances in
Algorithmic Differentiation",
editor = "Bruce Christianson and Shaun A. Forth and Andreas Griewank"
}
