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Numerical treatment of delay differential equations by Hermite Interpolation

  • Finite Difference Approximations of Solutions Periodic in Time of Hyperbolic Partial Differential Equations
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Summary

A class of numerical methods for the treatment of delay differential equations is developed. These methods are based on the wellknown Runge-Kutta-Fehlberg methods. The retarded argument is approximated by an appropriate multipoint Hermite Interpolation. The inherent jump discontinuities in the various derivatives of the solution are considered automatically.

Problems with piecewise continuous right-hand side and initial function are treated too. Real-life problems are used for the numerical test and a comparison with other methods published in literature.

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Authors and Affiliations

  1. Institut für Mathematik der Technischen Universität München, Arcisstr. 21, D-8000, München 2, Germany (Fed. Rep.)

    H. J. Oberle & H. J. Pesch

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  1. H. J. Oberle
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  2. H. J. Pesch
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Oberle, H.J., Pesch, H.J. Numerical treatment of delay differential equations by Hermite Interpolation. Numer. Math. 37, 235–255 (1981). https://doi.org/10.1007/BF01398255

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  • DOI: https://doi.org/10.1007/BF01398255

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