Publication: Using AD to Solve BVPs in Matlab
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Using AD to Solve BVPs in Matlab

- Article in a journal -
 

Author(s)
L. F. Shampine , Robert Ketzscher , Shaun A. Forth

Published in
ACM Transactions on Mathematical Software

Year
2005

Abstract
The Matlab program 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 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 bvp4cAD we have approached this ideal by a careful use of the MAD ad tool and some modification of bvp4c.

AD Tools
TOMLAB /MAD, MAD

BibTeX
@ARTICLE{
         Shampine2005UAt,
       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",
       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}.",
       month = "mar",
       ad_tools = "TOMLAB /MAD, MAD"
}


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