两点边值问题的一种精细求解方法  

A precise method for two-point boundary value problems

作　　者：富明慧[1] 张文志[1] 

机构地区：[1]中山大学,广州510275

出　　处：《应用力学学报》2010年第4期687-692,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(10672194);中俄NSFC-RFBR协议项目(10811120012)

摘　　要：将求解域均匀离散,由状态参量在相邻结点间的精细积分关系式,确定一组代数方程;并将其写成矩阵形式,代入边界条件后,代数方程组的系数矩阵可化为块三对角形式。针对这一特性,给出了一种高效的递推消元算法。由于没有离散误差,该方法具有较高的精度,不仅适用于任意边界的常规两点边值问题,还适用于奇异摄动边值问题。数值算例充分证明了本文方法的精度和效率。An efficient precise method for two-point boundary value problems is presented.Firstly,after dividing the interval evenly,a set of algebraic equations,which are written in the form of matrix,are determined by the precise integration relationships of the state parameters between the adjacent nodes.Then turn the coefficient matrices of the algebraic equations into block tridiagonal matrix form by substituting the boundary conditions into the equations.Considering the particular character of the equations,an efficient recursive method is given.The present method is of very high precision with no discrete error.The method can be used not only for conventional two-point boundary value problems of any form but also for singular perturbation problems.Numerical examples show the efficiency and the precision of the present method sufficiently.

关 键 词：一阶常微分方程 两点边值问题 精细积分法 递推方法 奇异摄动边值问题 

分 类 号：O241.81[理学—计算数学]