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 - <p style="text-align: justify;">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 <em>O</em>(<em>h<sup>4</sup></em>+<em>τ<sup>2</sup></em>) 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.</p>