| | | | | 非线性Schrdinger方程的守恒谱方法与拟谱方法 | | | 鲁百年 | | | 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。
【作者单位】：陕西师大数学系
【关键词】：非线性Schrdinger方程;谱方法;拟谱方法;收敛性;稳定性
【基金】：陕西师范大学青年科学基金
【DOI】：cnki:ISSN:1672-4291.0.1989-03-001
【正文快照】：
1问题与记号 本文考察如下一类非线性Sch1’6dinger方程的周期初值问题: }‘i“,一u二+日Iu!Zu一o;(x,t)〔R x J.(1·1) (1){u(x,o)=u。(戈);x任尺(1 .2) 火u(二+2二,:)=。(二,:);(二,:)〔二、J(1 .3)其中￡二、/二i,日为实数,。。为以2二为周期的己知复函数.、J=〔o,T」(T>0), | | | | | |  推荐 下载CAJ全文  下载PDF全文 | | | CAJViewer7.0阅读器支持所有CNKI文件格式，AdobeReader仅支持PDF格式 | | | | Spectral and Pseudo-spectral Methods for a Nonlinear Schrdinger Equation | | | Lu Bainian (Department of Mathematics) | | | 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.
【Keyword】：nonlinear schr(?)dinger equation;spectral and pseudo-spectral methods;convergence and stability. |
| | | | | | 1 | 王雨顺,秦孟兆; 2+1维Sine-Gordon方程多辛格式 [A];Fields, Gravity and Multisymplectic Structures--Proceedings of CCAST (World Laboratory) Workshop [C]; 2001年 |
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