奇摄动常微分方程系统的数值解法  

Numerical Solution for a System of Singularly Perturbed Ordinary Differential Equation

作　　者：蔡新[1] 

机构地区：[1]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2005年第2期168-171,共4页Journal of Xiamen University：Natural Science

基　　金：福建省自然科学基金(A04100021);集美大学科研基金(F03040)资助

摘　　要：讨论奇摄动常微分方程系统的二点边界值问题,这是奇摄动问题中较难的部分.文中介绍了多过渡点的选取方法,依此法构造不等距差分格式,在最大范数下证明新的差分格式关于摄动参数是一阶一致收敛.多过渡点确定了网格划分从细网格到中等网格和粗网格的过渡,而Shishkin Scheme (单过渡点法) 只将网格分为细网格和粗网格.多过渡点法很好地拟合了边界层的性质,在实际应用中相当有效,其收敛阶也高于Shishkin网格法.In this paper a two-point boundary value problem for a system of singularly perturbed ordinary differential problems is considered.It is the most complicated problem in singularly perturbed equation.The technique of select multi-transition points is introduced.According to multi-transition points method,non-equidistant difference scheme is constructed.In maximum norm,the new method is proved to be first-order uniform convergence with respected to the perturbed parameter.Multi-transition points determine the point of transition from fine mesh to middle and coarse mesh,while Shishkin scheme (single transition point method ) only determines the point of transition from fine to coarse mesh.It capture the properties of boundary layer efficiently.The new method is useful in practice application.The rate of convergence is higher than Shishkin’s scheme.

关 键 词：奇摄动 一致收敛 多过渡点 不等距网格 单过渡点法 多过渡点法 Shishkin网格法 

分 类 号：O241.81[理学—计算数学]