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One-step and extrapolation methods for differential-algebraic systems

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Summary

The paper analyzes one-step methods for differential-algebraic equations (DAE) in terms of convergence order. In view of extrapolation methods, certain perturbed asymptotic expansions are shown to hold. For the special DAE extrapolation solver based on the semi-implicit Euler discretization, the perturbed order pattern of the extrapolation tableau is derived in detail. The theoretical results lead to modifications of the known code. The efficiency of the modifications is illustrated by numerical comparisons over critical examples mainly from chemical combustion.

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Author notes

  1. J. Zugck

    Present address: Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293, D-6900, Heidelberg, Federal Republic of Germany

Authors and Affiliations

  1. Konrad-Zuse-Zentrum für Informationstechnik Berlin, Heilbronner Straße 10, D-1000, Berlin 31

    P. Deuflhard

  2. Section de Mathématiques, Université de Genève, 2-4 rue de Lièvre, CH-1211, Genève 24, Switzerland

    E. Hairer

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  1. P. Deuflhard
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  2. E. Hairer
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  3. J. Zugck
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Deuflhard, P., Hairer, E. & Zugck, J. One-step and extrapolation methods for differential-algebraic systems. Numer. Math. 51, 501–516 (1987). https://doi.org/10.1007/BF01400352

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