一类奇异两点边值问题的混合精细积分法  

A Mixed Precise Integration Method for a Class of Linear Singular Two Point Boundary Value Problems

作　　者：张文志 ZHANG Wen-zhi(School of Civil Engineering and Architecture,Wuyi University,Jiangmen 529020 China)

机构地区：[1]五邑大学土木建筑学院,广东江门529020

出　　处：《五邑大学学报（自然科学版）》2021年第3期67-72,共6页Journal of Wuyi University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11502172);广东省普通高校特色创新项目(2016KTSCX143);五邑大学科研启动项目(31013009)。

摘　　要：本文提出了求解一类奇异两点边值问题的混合精细积分法.首先,基于L.Hospital法则,将原问题在奇点加以改良.然后将整个求解区间分为[0,δ]和[δ,1],区间[0,δ]内的传递矩阵采用精细积分法求解,区间[δ,1]内的传递矩阵采用高阶乘法摄动法求解.最后通过递推消元法求解由各个子区间之间的相互关系建立的一组矩阵代数方程.数值算例证明了本文方法的有效性.In this paper,we present an improved precise integration method(PIM)for a class of singular two-point boundary value problems.Firstly,based on the L.Hospital rule,the original equation is improved at the singularity point.Then,the whole solution interval is divided into[0,δ] and [δ,1].The transfer matrix within the[0,δ] interval is solved by the precise integration method,and the transfer matrices within the [δ,1] interval are solved by the high order multiplication perturbation method(HOMPM).Finally,the reduction method is used to solve a set of matrix algebraic equations established by the relationship between each subinterval.Numerical examples show the validity of the present method.

关 键 词：奇异两点边值问题 精细积分法 高阶乘法摄动法 递推消元法 

分 类 号：O241.81[理学—计算数学]