非线性二阶变系数微分方程的三点边值问题
Three-point boundary value problems for nonlinear second-order variable coefficient differential equations
刘雪铃 1黄静1
作者信息
- 1. 亳州学院 电子与信息工程系,安徽 亳州 236800
- 折叠
摘要
研究了非线性二阶变系数微分方程的三点边值问题.首先,对非线性二阶变系数微分方程多次积分得到与之等价的Fredholm-Hammerstein积分方程;其次,利用分段泰勒级数得到Fredholm-Hammerstein积分方程的数值解;最后,通过具体算例验证此方法的可行性与有效性,并给出相应的误差估计.
Abstract
This paper deals with the three-point boundary value problem for nonlinear second-order variable coefficient differential equations.Firstly,the equivalent Fredholm-Hammerstein integral equations are obtained by integrating the non-linear second-order variable coefficient differential equations multiple times;secondly,the numerical solution of the Fred-holm-Hammerstein integral equations are gotten using piecewise taylor series;finally,the feasibility and effectiveness of this method are verified through specific examples,and corresponding error estimates are presented.
关键词
非线性二阶变系数微分方程/三点边值问题/Fredholm-Hammerstein积分方程/数值解/积分法Key words
Nonlinear second-order variable coefficient differential equation/Three-point boundary value problem/Fredholm-Hammerstein integral equation/Numerical solution/Integration method引用本文复制引用
基金项目
安徽省教育厅自然科学研究重点项目(2022AH052415)
安徽省教育厅自然科学研究项目(KJ2021A1150)
出版年
2024
NETL
NSTL
维普
万方数据