[1]谢烨,梁宗旗.非线性Schrdinger方程的五次B-样条逼近[J].集美大学学报(自然科学版),2015,20(2):145-153.
XIE Ye,LIANG Zong-qi.Numerical Approach of the Nonlinear Schrdinger Equation by the Quintic B-Spline[J].Journal of Jimei University,2015,20(2):145-153.
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非线性Schrdinger方程的五次B-样条逼近(PDF)
XIE Ye,LIANG Zong-qi.Numerical Approach of the Nonlinear Schrdinger Equation by the Quintic B-Spline[J].Journal of Jimei University,2015,20(2):145-153.
《集美大学学报（自然科学版）》[ISSN:1007-7405/CN:35-1186/N]
- 卷:
- 第20卷
- 期数:
- 2015年第2期
- 页码:
- 145-153
- 栏目:
- 数理科学与信息工程
- 出版日期:
- 2015-03-25
文章信息/Info
- Title:
- Numerical Approach of the Nonlinear Schrdinger Equation by the Quintic B-Spline
- Author(s):
- XIE Ye; LIANG Zong-qi
- School of Science,Jimei University,Xiamen 361021,China
- 关键词:
- 非线性Schrdinger方程; B-样条; 数值逼近; 孤立子
- Keywords:
- nonlinear Schrdinger equation; B-spline; numerical approach; soliton
- 分类号:
- -
- DOI:
- -
- 文献标志码:
- A
- 摘要:
- 利用五次B-样条配点有限元方法研究了经典的三次非线性Schrdinger方程.在该格式中，关于时间方向的离散是基于Crank-Nicolson差分格式，而空间方向采用了分片五次B-样条函数逼近，其得到的刚度矩阵是一个分块五对角型矩阵.同时，利用线性稳定性分析方法证明了该格式是无条件稳定的.通过数值例子，验证了该格式保持了方程的守恒性质及具有较高的精度，最后模拟了两个孤立子的碰撞.
- Abstract:
- In this paper,the quintic B-spline collocation finite element method is implemented to find numerical solution of the classic cubic nonlinear Schrdinger equation.The scheme is based on the Crank-Nicolson formulation for time discretization and quintic B-spline functions for space discretization,and the stiffness matrix of the scheme is a blockfivediagonal matrix.The scheme is verified to be unconditionally stable by the method of linear stability analysis.By numerical examples,it is confirmed that the scheme keeps the conservative property of the equation preferably.Finally,the collision of two solitons is simulated.
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更新日期/Last Update:
2015-06-01