Large Time-Stepping Spectral Methods for the Semiclassical Limit of the Defocusing Nonlinear Schrödinger Equation
We analyze a class of large time-stepping Fourier spectral methods for the semiclassical limit of the defocusing Nonlinear Schrödinger equation and provide highly stable methods which allow much larger time step than for a standard implicit-explicit approach. An extra term, which is consistent with...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/283959 |
| Summary: | We analyze a class of large time-stepping Fourier spectral methods for the semiclassical limit of the defocusing Nonlinear Schrödinger equation and provide highly stable methods which allow much larger time step than for a standard implicit-explicit approach. An extra term, which is consistent with the order of the time discretization, is added to stabilize the numerical schemes. Meanwhile, the first-order and second-order semi-implicit schemes are constructed and analyzed. Finally the numerical experiments are performed to demonstrate the effectiveness of the large time-stepping approaches. |
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| ISSN: | 1026-0226 1607-887X |