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Multi-value Numerical Methods for Hamiltonian Systems

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Numerical Mathematics and Advanced Applications - ENUMATH 2013

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 103))

Abstract

We discuss the effectiveness of multi-value numerical methods in the numerical treatment of Hamiltonian problems. Multi-value (or general linear) methods extend the well-known families of Runge-Kutta and linear multistep methods and can be considered as a general framework for the numerical solution of ordinary differential equations. There are some features that needs to be achieved by reliable geometric numerical integrators based on multi-value methods: G-symplecticity, symmetry and boundedness of the parasitic components. In particular, we analyze the effects of the mentioned features for the long term conservation of the energy and provide the numerical evidence confirming the theoretical expectations.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Salerno, Via Giovanni Paolo II, 132 – 84084, Fisciano, Italy

    Raffaele D’Ambrosio

Authors
  1. Raffaele D’Ambrosio
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Correspondence to Raffaele D’Ambrosio .

Editor information

Editors and Affiliations

  1. MATHICSE-ANMC, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Assyr Abdulle

  2. SB MATHICSE CMCS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Simone Deparis

  3. SB MATHICSE ANCHP, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Daniel Kressner

  4. SB MATHICSE CSQI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Fabio Nobile

  5. SB MATHICSE GR-PI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Marco Picasso

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D’Ambrosio, R. (2015). Multi-value Numerical Methods for Hamiltonian Systems. In: Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (eds) Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-319-10705-9_18

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