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

作　　者：刘雪铃 黄静 LIU Xueling;HUANG Jing(Bozhou College,Department of Electronic and Information Engineering,Bozhou Anhui 236800)

机构地区：[1]亳州学院电子与信息工程系,安徽亳州236800

出　　处：《宁夏师范学院学报》2024年第4期26-31,共6页Journal of Ningxia Normal University

基　　金：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项目(KJ2021A1150)。

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.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 nonlinear second-order variable coefficient differential equations multiple times;secondly,the numerical solution of the Fredholm-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 

分 类 号：O241.4[理学—计算数学]