Energy preserving integration of bi-Hamiltonian partial differential equations

B. Karasozen, G. Simsek

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    17 Citations (Scopus)
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    Abstract

    The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the long term preservation of the Hamiltonians and Casimir integrals, which is essential in simulating waves and solitons. Dispersive properties of the AVF integrator are investigated for the linearized equations to examine the nonlinear dynamics after discretization. (c) 2013 Elsevier Ltd. All rights reserved.
    Original languageEnglish
    Pages (from-to)1125-1133
    JournalApplied Mathematics Letters
    Volume26
    Issue number12
    DOIs
    Publication statusPublished - 2013

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