@Article{CiCP-20-5,
author = {},
title = {An Energy-Preserving Wavelet Collocation Method for General Multi-Symplectic Formulations of Hamiltonian PDEs},
journal = {Communications in Computational Physics},
year = {2016},
volume = {20},
number = {5},
pages = {1313--1339},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.231014.110416a},
url = {https://global-sci.com/article/80236/an-energy-preserving-wavelet-collocation-method-for-general-multi-symplectic-formulations-of-hamiltonian-pdes}
}