Numerical solutions of boundary value problems via fixed point iteration.

The aim of this paper is to solve second order nonlinear boundary value problems (BVPs) approximately. To do so, we utilize Thakur et al. iterative scheme (Filomat 3(10):2711- 2720, 2016) involving a weak contraction mapping in an arbitrary Banach space. Firstly, we study the convergence behaviour and the two numerical examples to show the better rate of convergence. Further, we apply this method to find the approximate solution of nonlinear boundary value problems (BVPs) and two illustrative numerical examples for BVPs are provided. Thus, several corresponding results in the literature are generalised and improved. [ABSTRACT FROM AUTHOR]