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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*
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:[email protected]
Email address:[email protected]
Email address:[email protected]
Email address:[email protected]
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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.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2012

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