The ultimate goal of this study is to implement a fixed point iterative scheme for the numerical solution of an extended class of nonlinear, nonlocal, elliptic boundary value problems. The method is based on applying well-known fixed point procedures such as Mann’s and Picard’s to a tailored linear integral that is expressed in terms of a Green’s function. A proof of convergence that utilizes the contraction principle is included. A number of test examples are presented to confirm the applicability, high accuracy and efficacy of the iterative process.

中文翻译：

---

一类非局部椭圆BVP的流体流动求解：一种迭代方法

这项研究的最终目标是为扩展的非线性，非局部，椭圆形边值问题的数值解实现不动点迭代方案。该方法基于将众所周知的不动点过程（如曼氏和皮卡德氏）应用于以格林函数表示的量身定制的线性积分。包含利用收缩原理的收敛性证明。给出了许多测试示例，以确认迭代过程的适用性，高精度和有效性。