Uniformly accurate oscillatory integrators for the Klein-Gordon-Zakharov system from low- to high-plasma frequency regimes
This work provides a numerical method for solving a challenging multi-scale PDE system, ensuring uniform accuracy across all frequency regimes, which is important for computational physics.
The authors develop a new class of oscillatory integrators for the Klein-Gordon-Zakharov system that achieve uniform accuracy across all plasma frequency regimes, from low to high, without step size restrictions. The methods are asymptotically consistent and converge to the Zakharov limit system as the plasma frequency tends to infinity.
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.