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二阶线性常微分方程的两点边值问题的泰勒展开式解法
引用本文:方敏,李显方.二阶线性常微分方程的两点边值问题的泰勒展开式解法[J].数学理论与应用,2006,26(3):74-76.
作者姓名:方敏  李显方
作者单位:湖南师范大学数学与计算机科学学院 长沙410081(方敏),中南大学土建学院力学与传感技术研究所 长沙410083(李显方)
摘    要:本文用泰勒展开公式求解二阶线性常微分方程的两点边值问题.首先将两点边值问题化为一个F redho lm积分方程,进一步通过泰勒展开公式化F redho lm积分方程为线性方程组,利用G ramm er法则可求得问题的近似解.

关 键 词:春勒展开式  二阶线性常微分方程  两点边值问题  近似解
收稿时间:12 29 2005 12:00AM

Taylor's expansion for solving two-point boundary value problems of second-order linear ordinary differential equation
Fang Min Li Xianfang.Taylor''''s expansion for solving two-point boundary value problems of second-order linear ordinary differential equation[J].Mathematical Theory and Applications,2006,26(3):74-76.
Authors:Fang Min Li Xianfang
Institution:1.College of Mathematics and Computer Science,Hunan Normal University,Changsha,410081;2.School of Civil Engineering and Architecture,Central South University,Chang,sha,410083
Abstract:Taylor's expansion is proposed to approximately solve two-point boundary value problems of second-order linear ordinary differential equations.First we transform the problems to a Fredholm integral equation,and then through Taylor's expansion the Fredholm integral equation is approximately converted to a system of linear equations.An approximate solution can be derived by using Crammer's rule.
Keywords:Taylor's expansion Second-roder linear ordinary differential equations Two-point boundary value problems Approximate solution
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