Large Time-Stepping Spectral Methods for the Semiclassical Limit of the Defocusing Nonlinear Schrödinger Equation

Abstract EN

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.