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Two-step fourth order methods for linear ODEs of the second order

Numerical Algorithms volume 51, pages 449–460 (2009)Cite this article

Abstract

A family of two step difference schemes of the fourth order has been developed for linear ODEs of the second order. Stability properties for such schemes are discussed and results of numerical tests are given. It is shown how the proposed technique can be extended to non-linear ODEs of second order.

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Authors and Affiliations

  1. Institute of System Dynamics and Control Theory, Sibirian Branch of the Russian Academy of Science, Irkutsk, Russia

    Mikhail V. Bulatov

  2. Department of Applied Mathematics and Computer Science, University of Gent, Gent, Belgium

    Guido Vanden Berghe

Authors
  1. Mikhail V. Bulatov
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  2. Guido Vanden Berghe
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Correspondence to Guido Vanden Berghe.

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Bulatov, M.V., Vanden Berghe, G. Two-step fourth order methods for linear ODEs of the second order. Numer Algor 51, 449–460 (2009). https://doi.org/10.1007/s11075-008-9249-9

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  • DOI: https://doi.org/10.1007/s11075-008-9249-9

Keywords

  • Difference schemes
  • Numerov method
  • P-stability