Novel Symplectic Discrete Singular Convolution Method for Hamiltonian PDEs

Novel Symplectic Discrete Singular Convolution Method for Hamiltonian PDEs

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.

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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

Keywords: