Discrete-time orthogonal spline collocation methods for the nonlinear Schrödinger equation with wave operator |
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Authors: | Shanshan Wang Luming Zhang Ran Fan |
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Affiliation: | College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China |
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Abstract: | In this paper, discrete-time orthogonal spline collocation schemes are proposed for the nonlinear Schrödinger 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. |
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Keywords: | Orthogonal spline collocation method Nonlinear Schrö dinger equation Wave operator Conserved quantity Convergence Stability |
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