@Article{Shampine:2005:UAS,
  author =       "L. F. Shampine and Robert Ketzscher and Shaun A. Forth",
  title =        "Using {AD} to Solve BVPs in {Matlab}",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "31",
  number =       "1",
  month =        mar,
  year =         "2005",
  pages =        "79--94",
  URL =          "http://doi.acm.org/10.1145/1055531.1055535", 
  abstract =     "The Matlab program {\tt bvp4c} solves two--point boundary
value problems (BVPs) 
                 of considerable generality.  The numerical
method requires partial derivatives of 
                 several kinds. To make
solving BVPs as easy as possible, the default in {\tt bvp4c} 
                 is
to approximate these derivatives with finite differences. The
solver is more 
                 robust and efficient if analytical derivatives are
supplied.  In this paper we 
                 investigate how to use automatic
differentiation (AD) to obtain the advantages of 
                 analytical
derivatives without giving up the convenience of finite
differences. 
                 In {\tt bvp4cAD} we have approached this ideal by
a careful use of the MAD AD tool 
                 and some modification of
{\tt bvp4c}.",
}