Solution of a Class of Nonlocal Elliptic BVPs Arising in Fluid Flow: An Iterative Approach

Abstract

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.