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Extrapolation applied to the method of characteristics for a first order system of two partial differential equations

Part one: The initial value problem

  • Handbook Series Approximations
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Summary

The proceduresivp presented in this paper calculates an approximate solution of Cauchy's initial value problem for hyperbolic systems of the form (1) (see below). The discretization which proceeds along the characteristics is performed using the midpoint rule started by Euler's method. To provide an algorithm of high accuracy the numerical solution is improved by step size extrapolation. This paper contains anAlgol program completed by examples of the use and test results.

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References

  1. Smith, R. R.: Extrapolation Applied to the Numerical Solution of Hyperbolic Partial Differential Equations. Dissertation, University of California, San Diego, 1970

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Authors and Affiliations

  1. Mathematisches Institut der Technischen Universität, Arcisstr. 21, D-8000, München 2, Bundesrepublik Deutschland

    W. Busch

  2. Mathematisches Institut der Universität, Weyertal 88, D-5000, Köln 41, Bundesrepublik Deutschland

    R. Esser &  W. Hackbusch

  3. Mathematisches Institut der Universität, Universitätsstr. 1, D-4000, Düsseldorf, Bundesrepublik Deutschland

    U. Herrmann

Authors
  1. W. Busch
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  2. R. Esser
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  3. W. Hackbusch
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  4. U. Herrmann
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Additional information

Editor's note: In this fascicle, prepublication of algorithms from the Approximations series of the Handbook for Automatic Computation is continued. Algorithms are published inAlgol 60 reference language as approved by the IFIP. Contributions in this series should be styled after the most recently published ones.

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Busch, W., Esser, R., Hackbusch, W. et al. Extrapolation applied to the method of characteristics for a first order system of two partial differential equations. Numer. Math. 24, 331–353 (1975). https://doi.org/10.1007/BF01397373

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  • DOI: https://doi.org/10.1007/BF01397373

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