Novel Symplectic Discrete Singular Convolution Method for Hamiltonian PDEs. (17th May 2016)

• Record Type: Journal Article
• Authors: Cai, Wenjun; Zhang, Huai; Wang, Yushun
• Is Part Of: Communications in computational physics. Volume 19:Number 5(2016:May)
• Page Start: 1375
• Page End: 1396
• Publication Date: 2016-05-17
• Subjects: 35Q55, -- 37K05, -- 65P10, -- 65M20, -- 65M70; Discrete singular convolution, -- differential matrix, -- symplectic integrator, -- Hamiltonian PDEs; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.scpde14.32s
• Languages: English
• ISSNs: 1815-2406

Abstract

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, bandlimited 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.