## 留言板

 引用本文: 张伟江. 一类非线性离散系统的指数二分性及其在数值分析和计算中的应用[J]. 应用数学和力学, 1992, 13(1): 81-88.
Zhang Wei-jiang. Exponential Dichotomies of Nonlinear Discrete Systems and Its Application to Numerical Analysis and Computation[J]. Applied Mathematics and Mechanics, 1992, 13(1): 81-88.
 Citation: Zhang Wei-jiang. Exponential Dichotomies of Nonlinear Discrete Systems and Its Application to Numerical Analysis and Computation[J]. Applied Mathematics and Mechanics, 1992, 13(1): 81-88.

## Exponential Dichotomies of Nonlinear Discrete Systems and Its Application to Numerical Analysis and Computation

• 摘要: 本文中我们考虑一类二阶非线性常微分方程的边值问题的迎风差分格式.我们运用奇异摄动方法构造了该迎风差分方程解的渐近近似,并利用指数二分性理论证明了有一个低阶方程其解是该迎风方程式的在边界外的一个良好近似.我们还构造了校正项,使校正项与低阶方程的解之和是一个渐近近似.最后一些数值例子用于显示本文方法的应用.
•  [1] Kopell,N.and G.B.Ermentrout,Symmetry and phase-locking in chains of weakly coupled scillators,Comm.Pure and Appl.Math,39(1986),623-660. [2] Dollan,E.P.,J.J.H.Miller and W.H.A.Schilders,Uniform Numerical Methods for Problems with Initial and Boundary Layers,Boole Press,Dublin(1980). [3] Miller,J.J.H.,(Ed.),An Introduction to Computational and Asymptotic Methods for Boundary and Interior Layers,Boole Press,Dublin(1982). [4] Kreiss,B.and H-O.Kreiss,Numerical methods for singular perturbation problems,SIAM J.Numer.Anal.,18(1981),262-276. [5] 苏煌城、吴启光.椭圆一双抛物偏微分方程奇异摄动问题的差分解法.应用数学和力学,1(2)(1980),187-176. [6] Abrahamsson,L.and S.Osher,Monotone difference schemes for singular perturbation problems,SIAM J.Numer.Anal.,19(1982),979-992. [7] Reinhardt,H.J.,Singular perturbation of difference methods for linear ordinary differential equations,Applied Analysis,10(1980),53-70. [8] Kopell,N.,W.Zhang and G.B.Ermentrout,Multiple coupling in chains of oscillators,SIAM J.Math.Anal.,4(1990). [9] Palmer,K.J.,Exponential dichotomies,the shadowing lemma and transversal homoclinic points,Dynamical Reported,1(1988),265-306. [10] O'Malley,R.E.,Jr.,An Introduction to Singular Perturbations,Academic Press,New York(1974).

##### 计量
• 文章访问数:  1561
• HTML全文浏览量:  18
• PDF下载量:  430
• 被引次数: 0
##### 出版历程
• 收稿日期:  1990-08-20
• 刊出日期:  1992-01-15

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈