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Analysis of higher order phase fitted variational integrators

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Abstract

In the present, the linear stability properties of the higher order phase fitted variational integrators are investigated. Towards this purpose, at first we calculate the eigenvalues of the amplification matrix for each method. Then, since the proposed integrators are derived specifically for the numerical integration of systems with oscillatory solutions, the linear stability analysis verifies their good behavior, when used for these problems. Finally, we test the proposed methods on several numerical examples, first with regard to their stability and secondly concerning the behavior in long term integration of highly oscillatory problems.

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Authors and Affiliations

  1. Chair of Applied Dynamics, University of Erlangen-Nuremberg, D-91058, Erlangen, Germany

    Odysseas Kosmas & Sigrid Leyendecker

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  1. Odysseas Kosmas
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  2. Sigrid Leyendecker
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Correspondence to Odysseas Kosmas.

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Communicated by: Axel Voigt

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Kosmas, O., Leyendecker, S. Analysis of higher order phase fitted variational integrators. Adv Comput Math 42, 605–619 (2016). https://doi.org/10.1007/s10444-015-9436-x

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  • DOI: https://doi.org/10.1007/s10444-015-9436-x

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