A conservative spectral collocation method for the nonlinear Schrödinger equation in two dimensions

Rongpei Zhang, Jiang Zhu, Xijun Yu, Mingjun Li and Abimael F.D. Loula

Applied Mathematics and Computation, 2017, vol. 310, issue C, 194-203

Abstract: In this study, we present a conservative Fourier spectral collocation (FSC) method to solve the two-dimensional nonlinear Schrödinger (NLS) equation. We prove that the proposed method preserves the mass and energy conservation laws in semi-discrete formulations. Using the spectral differentiation matrices, the NLS equation is reduced to a system of nonlinear ordinary differential equations (ODEs). The compact implicit integration factor (cIIF) method is later developed for the nonlinear ODEs. In this approach, the storage and CPU cost are significantly reduced such that the use of cIIF method becomes attractive for two-dimensional NLS equation. Numerical results are presented to demonstrate the conservation, accuracy, and efficiency of the method.

Keywords: Spectral collocation method; Nonlinear Schrödinger equation; Compact integration factor method; Conservation (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:310:y:2017:i:c:p:194-203

DOI: 10.1016/j.amc.2017.04.035

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