An Energy-Preserving Wavelet Collocation Method for General Multi-Symplectic Formulations of Hamiltonian PDEs

An Energy-Preserving Wavelet Collocation Method for General Multi-Symplectic Formulations of Hamiltonian PDEs

Year:    2016

Communications in Computational Physics, Vol. 20 (2016), Iss. 5 : pp. 1313–1339

Abstract

In this paper, we develop a novel energy-preserving wavelet collocation method for solving general multi-symplectic formulations of Hamiltonian PDEs. Based on the autocorrelation functions of Daubechies compactly supported scaling functions, the wavelet collocation method is conducted for spatial discretization. The obtained semi-discrete system is shown to be a finite-dimensional Hamiltonian system, which has an energy conservation law. Then, the average vector field method is used for time integration, which leads to an energy-preserving method for multi-symplectic Hamiltonian PDEs. The proposed method is illustrated by the nonlinear Schrödinger equation and the Camassa-Holm equation. Since differentiation matrix obtained by the wavelet collocation method is a cyclic matrix, we can apply Fast Fourier transform to solve equations in numerical calculation. Numerical experiments show the high accuracy, effectiveness and conservation properties of the proposed method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.231014.110416a

Communications in Computational Physics, Vol. 20 (2016), Iss. 5 : pp. 1313–1339

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:   

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