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Extrapolation to the limit for numerical solutions of hyperbolic equations

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Summary

The application of extrapolation to the limit requires the existence of an asymptotic expansion in powers of the step size. In this paper one-and multi-step methods for the solution of hyperbolic systems of first order are considered. Conditions are formulated that ensure the asymptotic expansion. Methods of characteristics for quasilinear systems with two independent variables are included in this presentation. If a rectangular grid is used, also non-quasilinear systems are admissible. The main part of this paper deals with initial value problems. But it is shown that in some exceptional cases asymptotic expansions hold for initial-boundary problems, too.

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Authors and Affiliations

  1. Mathematisches Institut der Universität zu Köln, Weyertal 86-90, D-5000, Köln 41, Germany (Fed. Rep.)

    W. Hackbusch

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  1. W. Hackbusch
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This paper is chiefly based on the author's doctoral thesis [7], written under the direction of Professor R. Bulirsch

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Hackbusch, W. Extrapolation to the limit for numerical solutions of hyperbolic equations. Numer. Math. 28, 455–474 (1977). https://doi.org/10.1007/BF01404347

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  • DOI: https://doi.org/10.1007/BF01404347

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