In the present paper, a new fixed point iterative method is introduced based on Green’s function and it’s successfully applied to approximate the solution of boundary value problems. A strong convergence result is proved for the integral operator by using the proposed method. It is also showed that the newly defined iterative method has a better rate of convergence than the Picard–Green’s, Mann–Green’s and Ishikawa–Green’s iterative methods. Some illustrative numerical examples are presented for the validity, applicability and high efficiency of the proposed iterative method. The results of this paper extend and generalize the corresponding results in the literature and particularly in Khuri and Louhichi (Appl Math Lett 82:50–57, 2018).

本文介绍了一种基于格林函数的不动点迭代新方法，并将其成功地应用于逼近边值问题的求解。利用该方法证明了积分算子的强收敛性。还表明，新定义的迭代方法比Picard-Green的，Mann-Green的和Ishikawa-Green的迭代方法具有更高的收敛速度。为了说明该迭代方法的有效性，适用性和高效率，给出了一些说明性的数值例子。本文的结果扩展并概括了文献中的相应结果，特别是在Khuri和Louhichi中（Appl Math Lett 82：50-57，2018）。