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Volume 12, Issue 5
Numerical Solutions of Coupled Nonlinear Schrödinger Equations by Orthogonal Spline Collocation Method

Qing-Jiang Meng, Li-Ping Yin, Xiao-Qing Jin & Fang-Li Qiao

DOI: 10.4208/cicp.180411.090112a

Commun. Comput. Phys., 12 (2012), pp. 1392-1416.

Published online: 2012-12

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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 O(h4+τ2) 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.

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@Article{CiCP-12-1392, author = {Qing-Jiang Meng, Li-Ping Yin, Xiao-Qing Jin and Fang-Li Qiao}, title = {Numerical Solutions of Coupled Nonlinear Schrödinger Equations by Orthogonal Spline Collocation Method}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {5}, pages = {1392--1416}, 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 O(h4+τ2) 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.180411.090112a}, url = {http://global-sci.org/intro/article_detail/cicp/7339.html} }
TY - JOUR T1 - Numerical Solutions of Coupled Nonlinear Schrödinger Equations by Orthogonal Spline Collocation Method AU - Qing-Jiang Meng, Li-Ping Yin, Xiao-Qing Jin & Fang-Li Qiao JO - Communications in Computational Physics VL - 5 SP - 1392 EP - 1416 PY - 2012 DA - 2012/12 SN - 12 DO - http://doi.org/10.4208/cicp.180411.090112a UR - https://global-sci.org/intro/article_detail/cicp/7339.html KW - AB -

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 O(h4+τ2) 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.

Qing-Jiang Meng, Li-Ping Yin, Xiao-Qing Jin and Fang-Li Qiao. (2012). Numerical Solutions of Coupled Nonlinear Schrödinger Equations by Orthogonal Spline Collocation Method. Communications in Computational Physics. 12 (5). 1392-1416. doi:10.4208/cicp.180411.090112a
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