Optimal error estimate of a compact scheme for nonlinear Schroedinger equation

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NETL
NSTL
Elsevier

外文摘要：It has been pointed out in literature that the symplectic scheme of a nonlinear Hamiltonian system can not preserve the total energy in the discrete sense Ge and Marsden (1988) [10]. Moreover, due to the difficulty in obtaining a priori estimate of the numerical solution, it is very hard to establish the optimal error bound of the symplectic scheme without any restrictions on the grid ratios. In this paper, we develop and analyze a compact scheme for solving nonlinear Schroedinger equation. We introduce a cut-off technique for proving optimal L~∞ error estimate for the compact scheme. We show that the convergence of the compact scheme is of second order in time and of fourth order in space. Meanwhile, we define a new type of energy functional by using a recursion relationship, and then prove that the compact scheme is mass and energy-conserved, symplectic-conserved, unconditionally stable and can be computed efficiently. Numerical experiments confirm well the theoretical analysis results.

外文关键词：

Nonlinear Schroedinger equationCompact schemeSymplectic schemeEnergy conservationOptimal error estimate

作者：

Jialin Hong、Lihai Ji、Linghua Kong、Tingchun Wang

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作者单位：

Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

School of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, China

School of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing, 210044, China

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出版年：

2017

DOI：

10.1016/j.apnum.2017.05.004

Applied numerical mathematics: Transactions of IMACS

ISSN：0168-9274

年,卷(期)：2017.120(Oct.)

被引量8
参考文献量27