论文标题
分裂步骤和哈密顿整合方法的比较，用于模拟非线性schrödinger方程
Comparison of Split-Step and Hamiltonian Integration Methods for Simulation of the Nonlinear Schrödinger Equation
论文作者
论文摘要
我们提供了两种数值方法的系统比较，以求解广泛使用的非线性Schrödinger方程。第一个是基于操作员拆分方法的标准二阶拆分步骤（SS2）方法。第二个是汉密尔顿整合方法（他）。它允许以隐式时间步进为代价对哈密顿量的确切保守。我们发现，在同一时间步骤中，他的数值错误在系统上比SS2解决方案小。同时，与仍然确保数值稳定性的SS2相比，他可以采取更大的时间步骤。相反，SS2时间步长受数值稳定性阈值的限制。
We provide a systematic comparison of two numerical methods to solve the widely used nonlinear Schrödinger equation. The first one is the standard second order split-step (SS2) method based on operator splitting approach. The second one is the Hamiltonian integration method (HIM). It allows the exact conservation of the Hamiltonian at the cost of requiring the implicit time stepping. We found that numerical error for HIM method is systematically smaller than the SS2 solution for the same time step. At the same time, one can take orders of magnitude larger time steps in HIM compared with SS2 still ensuring numerical stability. In contrast, SS2 time step is limited by the numerical stability threshold.
