Asymptotic preserving trigonometric integrators for the quantum Zakharov system

We present a new class of asymptotic preserving trigonometric integrators for the quantum Zakharov system. Their convergence holds in the strong quantum regime theta = 1 as well as in the classical regime theta -> 0 without imposing any step size restrictions. Moreover, the new schemes are asymptotic preserving and converge to the classical Zakharov system in the limit theta -> 0 uniformly in the time discretization parameter. Numerical experiments underline the favorable error behavior of the new schemes with first- and second-order time convergence uniformly in., first-order asymptotic convergence in. and long time structure preservation properties.

Automated summary

The new asymptotic preserving trigonometric integrators presented in the study are able to converge effectively in both quantum and classical regimes without imposing step size restrictions. Furthermore, they converge uniformly to the classical Zakharov system in the time discretization parameter. Numerical experiments demonstrate the favorable error behavior and long-term structure preservation properties of these new schemes.