Year: 2016
Communications in Computational Physics, Vol. 19 (2016), Iss. 5 : pp. 1375–1396
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.scpde14.32s
Communications in Computational Physics, Vol. 19 (2016), Iss. 5 : pp. 1375–1396
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
-
Conservative modified Crank–Nicolson and time-splitting wavelet methods for modeling Bose–Einstein condensates in delta potentials
Qian, Xu | Fu, Hao | Song, SongheApplied Mathematics and Computation, Vol. 307 (2017), Iss. P.1
https://doi.org/10.1016/j.amc.2017.02.037 [Citations: 2] -
A Review on the Discrete Singular Convolution Algorithm and Its Applications in Structural Mechanics and Engineering
Wang, Xinwei | Yuan, Zhangxian | Deng, JianArchives of Computational Methods in Engineering, Vol. 27 (2020), Iss. 5 P.1633
https://doi.org/10.1007/s11831-019-09365-5 [Citations: 9]