Energy-conserving Hamiltonian Boundary Value Methods for the numerical solution of the Korteweg-de Vries equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:351

Article

Brugnano, Luigi¹  Gurioli, Gianmarco¹  Sun, Yajuan^2,3 

[1] Univ Firenze, Dipartimento Matemat & Informat U Dini, Viale Morgagni 67-A, I-50134 Florence, Italy

[2] Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 1000190, Peoples R China

[3] Univ Chinese Acad Sci, Beijing 100049, Peoples R China

关键词: Korteweg-de Vries equation;    Hamiltonian partial differential equations;    Hamiltonian problems;    Energy-conserving methods;    Hamiltonian boundary value methods;    HBVMs;   

DOI  :  10.1016/j.cam.2018.10.014

来源: Elsevier

【 摘 要 】

In this paper we study the efficient solution of the well-known Korteweg-de Vries equation, equipped with periodic boundary conditions. A Fourier-Galerkin space semi-discretization at first provides a large-size Hamiltonian ODE problem, whose solution in time is then carried out by means of energy-conserving methods in the HBVM class (Hamiltonian Boundary Value Methods). The efficient implementation of the methods for the resulting problem is also considered and several numerical examples are reported. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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