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

基金项目: 国自然科学基金资助项目;国家教委优秀年轻教师基金资助

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.
- 非线性差分方程 /
- 奇异摄动 /
- 指数二分性
Abstract: In this pepar we consider the upwind difference scheme of a kind of boundary value problems for nonlinear,second order,ordinary differential equations.Singular perturbation method is applied to construct the asymptotic approximation of the solution to the upwind difference equation.Using the theory of exponential dichotomies we show that the solution of an order-reduced equation is a good approximation of the solution to the upwind difference equation except near boundaries.We construct correctors which yield asymptotic approximations by adding them to the solution of the order-reduced equation.Finally,some numerical examples are illustrated.
- Nonlinear difference equation /
- singular perturbation /
- exponential dichotomy

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