Abstract
Using average vector field method in time and Fourier pseudospectral method in space, we obtain an energy-preserving scheme for the nonlinear Schrödinger equation. We prove that the proposed method conserves the discrete global energy exactly. A deduction argument is used to prove that the numerical solution is convergent to the exact solution in discreteL2norm. Some numerical results are reported to illustrate the efficiency of the numerical scheme in preserving the energy conservation law.
Highlights
The nonlinear Schrodinger (NLS) equation describes a wide range of physical phenomena, such as hydrodynamics, plasma physics, nonlinear optics, self-focusing in laser pulses, propagation of heat pulses in crystals, and description of the dynamics of Bose-Einstein condensate at extremely low temperature [1, 2]
We derive a new method for the nonlinear Schrodinger system
We prove the proposed method preserves the energy conservation law exactly
Summary
The nonlinear Schrodinger (NLS) equation describes a wide range of physical phenomena, such as hydrodynamics, plasma physics, nonlinear optics, self-focusing in laser pulses, propagation of heat pulses in crystals, and description of the dynamics of Bose-Einstein condensate at extremely low temperature [1, 2]. It plays an essential role in mathematical and physical context, and more and more focus is concentrated upon its numerical solvers in recent years [3, 4].
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