Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 328, Issue -, Pages 354-370Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2016.10.022
Keywords
Nonlinear Schrodinger equation; Fourier pseudo-spectral method; Unconditional convergence; FFT
Funding
- China Postdoctoral Science Foundation [2016M591054, DMS-1200487]
- National Science Foundation [DMS-1200487, DMS-1517347]
- AFOSR [FA9550-12-1-0178]
- SC EPSCOR GEAR awards
- Jiangsu Collaborative Innovation Center for Climate Change
- National Natural Science Foundation of China [11271195, 41231173]
- Priority Academic Program Development of Jiangsu Higher Education Institutions
- NNSF of China [11201169]
- foundation of Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex [201606]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1517347] Funding Source: National Science Foundation
Ask authors/readers for more resources
A Fourier pseudo-spectral method that conserves mass and energy is developed for a two-dimensional nonlinear Schrodinger equation. By establishing the equivalence between the semi-norm in the Fourier pseudo-spectral method and that in the finite difference method, we are able to extend the result in Ref.[56] to prove that the optimal rate of convergence of the new method is in the order of O(N-r + tau(2)) in the discrete L-2 norm without any restrictions on the grid ratio, where N is the number of modes used in the spectral method and tau is the time step size. A fast solver is then applied to the discrete nonlinear equation system to speed up the numerical computation for the high order method. Numerical examples are presented to show the efficiency and accuracy of the new method. (C) 2016 Elsevier Inc. All rights reserved.
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