Uniformly accurate oscillatory integrators for the Klein-Gordon-Zakharov system from low- to high-plasma frequency regimes

TL;DR

This paper introduces new oscillatory integrators for the Klein-Gordon-Zakharov system that maintain accuracy across all plasma frequency regimes, including the high-frequency limit, without step size restrictions.

Contribution

The paper develops the first- and second-order uniformly accurate oscillatory integrators for the Klein-Gordon-Zakharov system, ensuring convergence from low to high plasma frequencies.

Findings

Convergence holds uniformly across plasma frequency regimes.

Numerical experiments confirm theoretical error estimates.

Integrators are asymptotic consistent with the Zakharov limit system.

Abstract

We present a novel class of oscillatory integrators for the Klein-Gordon-Zakharov system which are uniformly accurate with respect to the plasma frequency $c$. Convergence holds from the slowly-varying low-plasma up to 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 approximates 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.