论文标题
在正常或高度振荡状态下，最佳的收敛和长期保存Schrödinger方程的指数积分
Optimal convergence and long-time conservation of exponential integration for Schrödinger equations in a normal or highly oscillatory regime
论文作者
论文摘要
在本文中，我们在正常或高度振荡性方面应用于非线性schrödinger方程时制定和分析指数整合。一种具有能量保存，最佳收敛性和在动作保护，动量和密度保护的长期的指数积分器将得到制定和分析。为此，我们得出了连续阶段的指数积分器，并表明集成商可以准确保留汉密尔顿系统的能量。提出了三个实用的能源式集成商。结果表明，这些集成剂具有最佳的收敛性，并且在长时间内具有近乎行动，动量和密度的保护。进行了数值实验，以支持本文中提出的所有理论结果。还提供了集成商在其他类型的普通/部分微分方程中的某些应用。
In this paper, we formulate and analyse exponential integrations when applied to nonlinear Schrödinger equations in a normal or highly oscillatory regime. A kind of exponential integrators with energy preservation, optimal convergence and long time near conservations of actions, momentum and density will be formulated and analysed. To this end, we derive continuous-stage exponential integrators and show that the integrators can exactly preserve the energy of Hamiltonian systems. Three practical energy-preserving integrators are presented. It is shown that these integrators exhibit optimal convergence and have near conservations of actions, momentum and density over long times. A numerical experiment is carried out to support all the theoretical results presented in this paper. Some applications of the integrators to other kinds of ordinary/partial differential equations are also presented.
