Existence and approximation of solution for a nonlinear second-order three-point boundary value problem

Boundary value problems

Xian-Ci Zhong¹ 

[1] School of Mathematics and Information Science, Guangxi University, Nanning, P.R. China

关键词: three-point boundary value problems;    Hammerstein integral equation;    existence;    approximate solution;    convergence and error estimate;    34B10;    45B05;   

DOI  :  10.1186/s13661-016-0678-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

A nonlinear second-order ordinary differential equation with four cases of three-point boundary value conditions is studied by investigating the existence and approximation of solutions. First, the integration method is proposed to transform the considered boundary value problems into Hammerstein integral equations. Second, the existence of solutions for the obtained Hammerstein integral equations is analyzed by using the Schauder fixed point theorem. The contraction mapping theorem in Banach spaces is further used to address the uniqueness of solutions. Third, the approximate solution of Hammerstein integral equations is constructed by using a new numerical method, and its convergence and error estimate are analyzed. Finally, some numerical examples are addressed to verify the given theorems and methods.

【 授权许可】

CC BY