We present a new class of asymptotic preserving trigonometric integrators for the quantum Zakharov system. Their convergence holds in the strong quantum regime $$\vartheta = 1$$ ϑ = 1 as well as in the classical regime $$\vartheta \rightarrow 0$$ ϑ → 0 without imposing any step size restrictions. Moreover, the new schemes are asymptotic preserving and converge to the classical Zakharov system in the limit $$\vartheta \rightarrow 0$$ ϑ → 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 $$\vartheta $$ ϑ , first-order asymptotic convergence in $$\vartheta $$ ϑ and long time structure preservation properties.

中文翻译：

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量子 Zakharov 系统的渐近保持三角积分器

我们为量子 Zakharov 系统提出了一类新的渐近保持三角积分器。它们的收敛性在强量子机制 $$\vartheta = 1$$ ϑ = 1 以及经典机制 $$\vartheta \rightarrow 0$$ ϑ → 0 中成立，而没有施加任何步长限制。此外，新方案是渐近保持的，并且在时间离散化参数中均匀地收敛到极限 $$\vartheta \rightarrow 0$$ ϑ → 0 中的经典 Zakharov 系统。数值实验强调了具有一阶和二阶时间一致收敛于 $$\vartheta $$ϑ 的一阶和二阶时间收敛、$$\vartheta $$ϑ 中的一阶渐近收敛和长时间结构保存特性的新方案的有利误差行为。