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Automatic differentiation
of numerical integration algorithms

Authors: Peter Eberhard and Christian Bischof
Journal: Math. Comp. 68 (1999), 717-731
MSC (1991): Primary 34A12, 65L05, 65L06; Secondary 68N99
MathSciNet review: 1613703
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Abstract | References | Similar Articles | Additional Information

Abstract: Automatic differentiation (AD) is a technique for automatically augmenting computer programs with statements for the computation of derivatives. This article discusses the application of automatic differentiation to numerical integration algorithms for ordinary differential equations (ODEs), in particular, the ramifications of the fact that AD is applied not only to the solution of such an algorithm, but to the solution procedure itself. This subtle issue can lead to surprising results when AD tools are applied to variable-stepsize, variable-order ODE integrators. The computation of the final time step plays a special role in determining the computed derivatives. We investigate these issues using various integrators and suggest constructive approaches for obtaining the desired derivatives.

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Additional Information

Peter Eberhard
Affiliation: Institute B of Mechanics, University of Stuttgart, 70550 Stuttgart, Germany

Christian Bischof
Affiliation: Rheinisch-Westfälische Technische Hochschule Aachen, Seffenter Weg 23, D-52056 Aachen, Germany

Received by editor(s): November 11, 1996
Received by editor(s) in revised form: July 24, 1997
Additional Notes: This work was partially completed while the first author was visiting the Department of Mechanical Engineering at the University of California at Berkeley supported by the German Research Council (DFG) under grant EB195/1-1.
The second author was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under contract W-31-109-Eng-38.
Article copyright: © Copyright 1999 American Mathematical Society