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We present a novel class of oscillatory integrators for the Klein--Gordon--Zakharov system which are uniformly accurate with respect  the plasma frequency $c$. Convergence holds from the slowly varying low-plasma up  the highly oscillatory high-plasma frequency regimes without any step size restriction and, especially, uniformly in $c$. The introduced schemes are moreover asymptotic consistent and approximate the solutions of the corresponding Zakharov limit system in the high-plasma frequency limit ($c to infty$). We in particular present the construction of the first- and second-order uniformly accurate oscillatory integrators and establish rigorous, uniform error estimates. Numerical experiments underline our theoretical convergence results.

Uniformly Accurate Oscillatory Integrators for the Klein--Gordon--Zakharov System from Low- to High-Plasma Frequency Regimes