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We present a uniformly and optimally accurate numerical method for solvingthe Klein-Gordon-Zakharov (KGZ) system with two dimensionless parameters$0<\epsilon\le1$ and $0<\gamma\le 1$, which are inversely proportional to theplasma frequency and the acoustic speed, respectively. In the simultaneoushigh-plasma-frequency and subsonic limit regime, i.e. $\epsilon<\gamma\to 0^+$,the KGZ system collapses to a cubic Schr\"odinger equation, and the solutionpropagates waves with $O(\epsilon^2)$-wavelength in time and meanwhile containsrapid outgoing initial layers with speed $O(1/\gamma)$ in space due to theincompatibility of the initial data. By presenting a multiscale decompositionof the KGZ system, we propose a multiscale time integrator Fourierpseduospectral method which is explicit, efficient and uniformly accurate forsolving the KGZ system for all $0<\epsilon<\gamma\leq1$. Numerical results arereported to show the efficiency and accuracy of scheme. Finally, the method isapplied to investigate the convergence rates of the KGZ system to its limitingmodels when $\epsilon<\gamma\to 0^+$.

A uniformly and optimally accurate method for the Klein-Gordon-Zakharov system in simultaneous high-plasma-frequency and subsonic limit regime