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

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 Schr ¨odinger 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 Oh4+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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