An Energy-Preserving Wavelet Collocation Method for General Multi-Symplectic Formulations of Hamiltonian PDEs. (2nd November 2016)

• Record Type: Journal Article
• Authors: Gong, Yuezheng; Wang, Yushun
• Is Part Of: Communications in computational physics. Volume 20:Number 5(2016:Nov.)
• Page Start: 1313
• Page End: 1339
• Publication Date: 2016-11-02
• Subjects: 65M06, -- 65M70, -- 65T50, -- 65Z05; Energy-preserving, -- average vector field method, -- wavelet collocation method, -- nonlinear Schrödinger equation, -- Camassa-Holm equation; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.231014.110416a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.