Using AD to solve BVPs in MATLAB
Lawrence F. Shampine, Robert Ketzscher & Shaun A. Forth
Published in
ACM Transactions on Mathematical Software (TOMS), Volume 31 , Issue 1
(March 2005) pp 79-94
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 article 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.
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ACM Portal Entry: http://doi.acm.org/10.1145/1055531.1055535