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Generating functions of multi-symplectic RK methods via DW Hamilton–Jacobi equations

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Abstract

The De Donder–Weyl (DW) Hamilton–Jacobi equation is investigated in this paper, and the connection between the DW Hamilton–Jacobi equation and multi-symplectic Hamiltonian system is established. Based on the DW Hamilton–Jacobi theory, generating functions for multi-symplectic Runge–Kutta (RK) methods and partitioned Runge–Kutta (PRK) methods are presented.

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Authors and Affiliations

  1. LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, China

    Jialin Hong & Yajuan Sun

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  1. Jialin Hong
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  2. Yajuan Sun
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Correspondence to Yajuan Sun.

Additional information

The work is supported by the Foundation of ICMSEC, LSEC, AMSS and CAS, the NNSFC (No.10501050, 19971089 and 10371128) and the Special Funds for Major State Basic Research Projects of China (2005CB321701).

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Hong, J., Sun, Y. Generating functions of multi-symplectic RK methods via DW Hamilton–Jacobi equations. Numer. Math. 110, 491–519 (2008). https://doi.org/10.1007/s00211-008-0170-x

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  • DOI: https://doi.org/10.1007/s00211-008-0170-x

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