@Article{CiCP-19-1375,
author = {Wenjun Cai, Huai Zhang and Yushun Wang},
title = {Novel Symplectic Discrete Singular Convolution Method for Hamiltonian PDEs},
journal = {Communications in Computational Physics},
year = {2018},
volume = {19},
number = {5},
pages = {1375--1396},
abstract = {<p style="text-align: justify;">This paper explores the discrete singular convolution method for Hamiltonian
PDEs. The differential matrices corresponding to two delta type kernels of the
discrete singular convolution are presented analytically, which have the properties of
high-order accuracy, band-limited structure and thus can be excellent candidates for the
spatial discretizations for Hamiltonian PDEs. Taking the nonlinear Schrödinger equation
and the coupled Schrödinger equations for example, we construct two symplectic
integrators combining this kind of differential matrices and appropriate symplectic
time integrations, which both have been proved to satisfy the square conservation
laws. Comprehensive numerical experiments including comparisons with the central
finite difference method, the Fourier pseudospectral method, the wavelet collocation
method are given to show the advantages of the new type of symplectic integrators.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.scpde14.32s},
url = {http://global-sci.org/intro/article_detail/cicp/11134.html}
}