Comparison of numerical methods for the Zakharov system in the subsonic limit regime

摘要

We compare numerically spatial/temporal resolution of various methods for solving the Zakharov system (ZS) in the subsonic limit regime, which involves a small parameter 0<ε≤1 inversely proportional to the acoustic speed. In this regime, i.e., 0<ε≪1, the solution presents highly oscillatory initial layers due to the wave operator or the incompatibility of the initial data. Specifically, the solution propagates waves with wavelength of O(ε) and O(1) in time and space, respectively. By applying the sine pseudospectral discretization for spatial derivatives followed by a time-splitting technique for integrating the Schrödinger equation combined with an exponential wave integrator in phase space for integrating the wave equation, we propose four different numerical methods for the ZS based on different quadrature rules for approximating the integral or some property of conservation. Numerical results suggest that all the methods are spectrally accurate in space, which is uniformly for ε∈(0,1]. For temporal error, the best method converges uniformly with linear convergence rate at O(τ) in the subsonic limit regime.