We present a uniformly first order accurate numerical method for solving the Klein-Gordon-Zakharov (KGZ) system with two dimensionless parameters $0<\epsilon \le 1$ and $0<\gamma \le 1$, which are inversely proportional to the plasma frequency and the acoustic speed, respectively. In the simultaneous high-plasma-frequency and subsonic limit regime, i.e. $\epsilon <\gamma \to 0^{+}$, the KGZ system collapses to a cubic Schrödinger equation, and the solution propagates waves with $O({\epsilon }^2)$-wavelength in time and meanwhile contains rapid outgoing initial layers with speed $O(1/\gamma )$ in space due to the incompatibility of the initial data. By presenting a multiscale decomposition of the KGZ system, we propose a multiscale time integrator Fourier pseudospectral method which is explicit, efficient and uniformly accurate for solving the KGZ system for all $0<\epsilon <\gamma \le 1$. Numerical results are reported to show the efficiency and accuracy of scheme. Finally, the method is applied to investigate the convergence rates of the KGZ system to its limiting models when $\epsilon <\gamma \to 0^{+}$.

我们提出了一种统一的一阶精确数值方法，用于求解带有两个无量纲参数的Klein-Gordon-Zakharov（KGZ）系统 $0<\epsilon \le \mathrm{1个}$ 和 $0<\gamma \le \mathrm{1个}$分别与等离子频率和声速成反比。在同时的高等离子频率和亚音速极限状态下，即$\epsilon <\gamma \to 0^{+}$，KGZ系统坍缩成三次Schrödinger方程，并且解以 $Ø（{\epsilon }^2）$-时间上的波长，同时包含快速的外出初始层 $Ø（\mathrm{1个}/\gamma ）$由于初始数据不兼容而在空间上造成的。通过提出KGZ系统的多尺度分解，我们提出了一种多尺度时间积分器傅里叶伪谱方法，该方法显式，高效且一致准确，可以解决所有问题的KGZ系统。$0<\epsilon <\gamma \le \mathrm{1个}$。数值结果表明该方案的有效性和准确性。最后，将该方法应用于研究KGZ系统到极限模型时的收敛速度。$\epsilon <\gamma \to 0^{+}$。