Discrete-time orthogonal spline collocation methods for the nonlinear Schrodinger equation with wave operator

作者：Wang Shanshan; Zhang Luming^*; Fan Ran

来源：Journal of Computational and Applied Mathematics, 2011, 235(8): 1993-2005.

DOI：10.1016/j.cam.2010.09.025

• Orthogonal spline collocation method
• Nonlinear Schrodinger equation
• Wave operator
• Conserved quantity
• Convergence
• Stability

In this paper, discrete-time orthogonal spline collocation schemes are proposed for the nonlinear Schrodinger equation with wave operator. These schemes are constructed by using orthogonal spline collocation approaches combined with finite difference methods. The conservative property, the convergence, and the stability of these methods are theoretically analyzed and also verified by extensive numerical experiments. In addition, some interesting phenomena which require further theoretical analysis are discussed numerically.

• 出版日期2011-2-15
• 单位南京航空航天大学