| 非线性Schrdinger方程的守恒谱方法与拟谱方法 |
| |
| 引用本文： | 鲁百年.非线性Schrdinger方程的守恒谱方法与拟谱方法[J].陕西师范大学学报,1989(3). |
| |
| 作者姓名： | 鲁百年 |
| |
| 作者单位： | 陕西师大数学系 |
| |
| 基金项目： | 陕西师范大学青年科学基金 |
| |
| 摘 要： | 本文考察一类非线性SchrSdinger方程的谱方法与拟谱方法,构造了一类无条件稳定的全离散格式,证明了L~2模的收敛性与稳定性。该全离散格式为线性方程组,它既具备Crank-Nicolson格式(非线性方程组)的稳定性,又具备相同的精度,容易在计算机上实现。所以,较Crank-Nic01son格式优越。最后讨论了一致模的收敛性与稳定性。
|
| 关 键 词： | 非线性Schrdinger方程 谱方法 拟谱方法 收敛性 稳定性 |
Spectral and Pseudo-spectral Methods for a Nonlinear Schrdinger Equation |
| |
| Lu Bainian.Spectral and Pseudo-spectral Methods for a Nonlinear Schrdinger Equation[J].Journal of Shaanxi Normal University: Nat Sci Ed,1989(3). |
| |
| Authors: | Lu Bainian |
| |
| Institution: | Department of Mathematics |
| |
| Abstract: | In this paper, an unconditionally stable spectral and pseudo-spectral methods for a nonlinear Schrdinger equation are presented. Convergence and stability in L~2-norm are proved for both spectral and pseudo-spectral approximations. The pseudo-spectral method which is an algebrically linear system is possessed of the same accuracy and stability of Crank-Nicolson scheme which is an algebrically nonlinear system. And it is easily performed on computers. Therefore, the author's schemes are better than Crank-Nicolson scheme. Moreover, convergence and stability in uniform norm are discussed. |
| |
| Keywords: | nonlinear schr(?)dinger equation spectral and pseudo-spectral methods convergence and stability |
| 本文献已被 CNKI 等数据库收录！ |
