Using AD to solve BVPs in MATLAB

Authors:
L. F. Shampine;Robert Ketzscher;Shaun A. Forth
Affiliations:
Southern Methodist University, Dallas, TX;Cranfield University (Shrivenham Campus), Swindon, United Kingdom;Cranfield University (Shrivenham Campus), Swindon, United Kingdom
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2005

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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.