差分方程奇异摄动问题的一种渐近方法  

AN ASYMPTOTIC METHOD FOR SINGULAR PERTURBATION PROBLEMS OF DIFFERENCE EQUATIONS

作　　者：吴启光[1] 

机构地区：[1]南京大学

出　　处：《高等学校计算数学学报》1990年第1期43-53,共11页Numerical Mathematics A Journal of Chinese Universities

摘　　要：关于微分方程奇异摄动问题的研究已有大量的文献和专著,有比较系统的理论以及若干比较有效的方法。 在数字模拟、样本数据控制系统、计算机的自适应控制系统以及经济学、生物学等领域的许多问题和含小参数的微分方程离散化以后所得到的差分方程均将出现含有小参数的差分方程问题。In this paper,we consider the singular perturbation problems of difference equations with a small parameter,when ?equals to zero,the original equation -are degenerated into the lower order difference equation.Author constructed a new asymptotic method,which consists of the following steps,(i) solve the reduced problem.(ii) put the solution of the reduced problem into the lowest order term of the original difference equation,then we demand that the solution of this equation satisfy the boundary condition which is lost.Whe tends to zero,the solution of this equation approaches to the solution of the reduced problem.Finally,we take the solution of this equation as an asymptotic solution of the original difference equation problem.

关 键 词：差分方程 奇异摄动问题 渐近方法 

分 类 号：O241.84[理学—计算数学]