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On the properties of Runge-Kutta discrete adjoints. (English) Zbl 1157.65421
Alexandrov, Vassil N. (ed.) et al., Computational science – ICCS 2006. 6th international conference, Reading, UK, May 28–31, 2006. Proceedings, Part IV. Berlin: Springer (ISBN 3-540-34385-7/pbk). Lecture Notes in Computer Science 3994, 550-557 (2006).
Summary: In this paper we analyze the consistency and stability properties of Runge-Kutta discrete adjoints. Discrete adjoints are very popular in optimization and control since they can be constructed automatically by reverse mode automatic differentiation. The consistency analysis uses the concept of elementary differentials and reveals that the discrete Runge-Kutta adjoint method has the same order of accuracy as the original, forward method. A singular perturbation analysis reveals that discrete adjoints of stiff Runge-Kutta methods are well suited for stiff problems.
For the entire collection see [Zbl 1107.68001].

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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