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Numerical Solutions of Coupled Nonlinear Schrödinger Equations by Orthogonal Spline Collocation Method

Published online by Cambridge University Press:  20 August 2015

Qing-Jiang Meng ,
Li-Ping Yin ,
Xiao-Qing Jin  and
Fang-Li Qiao
Qing-Jiang Meng*
Affiliation:
Department of Mathematics, University of Macau, Macao
Li-Ping Yin*
Affiliation:
First Institute of Oceanography, State Oceanic Administration, Qingdao, Shandong 266061, China & College of Physical and Environmental Ocanography, Ocean University of China, Qingdao, Shandong 266003, China
Xiao-Qing Jin*
Affiliation:
Department of Mathematics, University of Macau, Macao
Fang-Li Qiao*
Affiliation:
Key Laboratory of Marine Science and Numerical Modeling of State Oceanic Administration & First Institute of Oceanography, State Oceanic Administration, Qingdao, Shandong 266061, China
*
Corresponding author.Email address:qjmeng04@163.com
Email address:lipyconstance@163.com
Email address:xqjin@umac.mo
Email address:qiaofl@fio.org.cn
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Abstract

In this paper, we present the use of the orthogonal spline collocation method for the semi-discretization scheme of the one-dimensional coupled nonlinear Schrödinger equations. This method uses the Hermite basis functions, by which physical quantities are approximated with their values and derivatives associated with Gaussian points. The convergence rate with order and the stability of the scheme are proved. Conservation properties are shown in both theory and practice. Extensive numerical experiments are presented to validate the numerical study under consideration.

Keywords

65N3535C4535L65Coupled nonlinear Schrödinger equationsorthogonal spline collocation methodconservation law
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 5 , November 2012 , pp. 1392 - 1416
Copyright
Copyright © Global Science Press Limited 2012

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