含阻尼效应的非线性薛定谔方程的共形分裂高阶紧致差分格式

该文对含有阻尼效应的非线性薛定谔方程提出了一个新的共形分裂高阶紧致差分格式.首先利用分裂技巧,将复杂方程分裂为3个子问题; 然后对于其中的非线性子问题,利用其逐点质量守恒的性质可以精确求解,避免了迭代,提高了计算效率; 再利用了高阶紧致方法对空间进行离散,在基本不提高成本的情况下,提升了空间精度; 最后通过理论分析与数值实验证明了该格式的高精度、稳定性以及保持共形质量守恒律.

The Conformal Splitting High-Order Compact Difference Scheme for Damped Nonlinear Schrödinger Equation

The new conformal splitting high-order compact difference scheme for damped nonlinear Schrödinger equation is proposed in this paper.Firstly,the complex equation is divided into three subproblems by using the splitting technique.Then,the nonlinear subproblem can be solved precisely by using the property of point-by-point mass conservation,which avoids iteration and improves computational efficiency.In addition,the high-order compact method is applied to discretize the space,which improves the spatial accuracy without increasing the cost.Finally,the high accuracy,stability and two conformal conservation laws of the scheme are proved by theoretical analysis and numerical experiments.