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 and Fang-Li Qiao

10.4208/cicp.180411.090112a

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

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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 Schro¨dinger equations. This method uses the Hermite basis functions, by which physical quantities areapproximatedwiththeir valuesand derivativesassociatedwith 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. 

  • History

Published online: 2012-12

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