|
|||||
|
|
| 二维非线性Schr(o)dinger方程的辛与多辛格式 | |
| 引用本文： | 朱华君,陈亚铭,宋松和,唐贻发.二维非线性Schr(o)dinger方程的辛与多辛格式[J].计算数学,2010,32(3):315-326. |
| 作者姓名： | 朱华君 陈亚铭 宋松和 唐贻发 |
| 作者单位： | 1. 国防科学技术大学数学与系统科学系,长沙,410073 2. 中科院数学与系统科学系,北京,100080 |
| 基金项目： | 国家自然科学基金(10971226)和民口973课题(2009CB723802-4)资助项目 |
| 摘 要： | 对满足周期边界条件的二维非线性Schrödinger方程,运用中心差分对该方程进行空间离散, 得到一个有限维Hamilton系统,然后用隐式Euler中点格式进行时间离散得到其辛格式. 针对该方程的多辛形式, 运用有限体积法离散,得到一种直平行六面体上的中点型多辛格式. 用所构造的辛与多辛格式对二维非线性Schrödinger方程的平面波解和奇异解进行数值模拟,结果验证了所构 造格式的有效性. 最后, 根据计算结果,对两种格式进行了分析和比较.
|
| 关 键 词： | 二维非线性Shrö dinger方程 辛格式 有限体积法 多辛格式 |
| 收稿时间： | 2009-11-09 |
SYMPLECTIC AND MULTI-SYMPLECTIC SCHEMES FOR THE TWO-DIMENSIONAL NONLINEAR SCHR(o)DINGER EQUATION |
|
| Zhu Huajun,Chen Yaming,Song Songhe,Tang Yifa.SYMPLECTIC AND MULTI-SYMPLECTIC SCHEMES FOR THE TWO-DIMENSIONAL NONLINEAR SCHR(o)DINGER EQUATION[J].Mathematica Numerica Sinica,2010,32(3):315-326. | |
| Authors: | Zhu Huajun Chen Yaming Song Songhe Tang Yifa |
| Institution: | 1. College of Science, National University of Defense Technology, Changsha 410073, China; 2. Academy of Mathematics Systems Science, Chinese Academy of Science, Beijing 100080, China |
| Abstract: | The two-dimensional nonlinear Schrödinger equation (2D NLSE) with periodic boundary condition is considered in this paper. An implicit symplectic scheme is constructed by using central difference scheme in space and implicit Euler-centered scheme in time. In addition, a midpoint rule multi-symplectic method is obtained by applying a cell vertex finite volume discretization to its multi-symplectic form. Numerical simulations are presented for plane wave solution and singular solution of the 2D NLSE. The results demonstrate the effectiveness of the proposed methods. Furthermore, the two methods are analyzed and compared with each other. |
| Keywords: | |
| 本文献已被 万方数据 等数据库收录！ | |
| 点击此处可从《计算数学》浏览原始摘要信息 | |
| 点击此处可从《计算数学》下载免费的PDF全文 | |