BibTeX
@ARTICLE{
         Charpentier2018Taf,
       crossref = "Christianson2018Sio",
       author = "Isabelle Charpentier and Bruno Cochelin",
       title = "Towards a full higher order {AD}-based continuation and bifurcation framework",
       journal = "Optimization Methods \& Software",
       volume = "33",
       number = "4--6",
       pages = "945--962",
       year = "2018",
       publisher = "Taylor \& Francis",
       doi = "10.1080/10556788.2018.1428604",
       url = "https://doi.org/10.1080/10556788.2018.1428604",
       eprint = "https://doi.org/10.1080/10556788.2018.1428604",
       abstract = "Some of the theoretical aspects of continuation and bifurcation methods devoted to
         the solution for nonlinear parametric systems are presented in a higher order automatic
         differentiation (HOAD) framework. Besides, benefits in terms of generality and ease of use, HOAD is
         used to assess fold and simple bifurcations points. In particular, the formation of a geometric
         series in successive Taylor coefficients allows for the implementation of an efficient detection and
         branch switching method at simple bifurcation points. Some comparisons with the Auto and MatCont
         continuation software are proposed. Strengths are then exemplified on a classical case study in
         structural mechanics.",
       booktitle = "Special issue of Optimization Methods \& Software: Advances in
         Algorithmic Differentiation",
       editor = "Bruce Christianson and Shaun A. Forth and Andreas Griewank"
}