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

Authors:
Shanshan Wang;Luming Zhang;Ran Fan
Affiliations:
-;-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

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.