@Article{CiCP-20-1313, author = {}, title = {An Energy-Preserving Wavelet Collocation Method for General Multi-Symplectic Formulations of Hamiltonian PDEs}, journal = {Communications in Computational Physics}, year = {2018}, volume = {20}, number = {5}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.231014.110416a}, url = {http://global-sci.org/intro/article_detail/cicp/11191.html} }