二维非线性Schr?dinger方程的两类局部守恒算法

Numerical analysis of two local conservative methods for two-dimensional nonlinear Schr?dinger equation

本文针对二维非线性Schr?dinger方程,提出两类局部守恒算法.不需要考虑边界条件,即可保持任意时空区域上相应的局部能量守恒律和局部动量守恒律.在合适的边界条件下,它们能自然地保持电荷、全局能量或全局动量守恒律.本文同时对算法进行了守恒分析和误差分析.在数值实验部分,本文构造了类似的多辛Preissman算法进行比较,数值结果验证了其长时间计算的优势.

In this paper, we propose two local conservative methods for solving two-dimensional nonlinear Schr？dinger equation. Without consideration of the boundary conditions, they can preserve corresponding local energy and momentum conservation laws exactly at arbitrary spatial-temporal regions. Meanwhile, the charge,global energy and global momentum conservation laws can be conserved under suitable boundary conditions.Numerical analysis, including conservative properties and error estimation analysis, are investigated. Furthermore, a similar multi-symplectic Preissman scheme is constructed as comparison. Numerical experiments show the advantages of the proposed methods during long-time numerical simulations and validate the analysis.