摘要
将求解区间上部分节点的Lgrange插值,通过加权可以构造出一类重心型有理插值函数。重心型有理插值函数在整个区间上具有无穷次光滑性,且不存在极点。本文利用重心型有理插值函数作为试函数,采用Galerkin法提出了求解线性常微分方程两点边值问题的一种新型数值方法。给出了数值计算公式和数值实施流程。数值算例验证了本文方法的有效性和计算精度。
With weighted Lagrangian interpolation of partial points, one can construct a family of barycentric rational interpolations that have no poles and arbitrary high approximation orders, regardless of the distribution of the points. In this paper, using Galerkin method and barycentric rational interpolations as trial functions, a new type of numerical method is presented for solving boundary value problems of second order linear ODE. The formulations of the proposed method are given. The numerical results are presented to demonstrate the effectiveness and accuracy of the proposed method. The numerical results are presented to demonstrate the effectiveness and accuracy of proposed method.
出处
《山东建筑大学学报》
2008年第4期283-286,共4页
Journal of Shandong Jianzhu University
基金
国家自然科学基金专项基金资助项目(50727904)
山东建筑大学科研基金资助项目(XN050103)
关键词
重心有理插值
常微分方程
两点边值问题
GALERKIN法
barycentric rational interpolation
ordinary differential equation
boundary value problem
Galerkin method
