A new fixed point approximation method for solving third-order BVPs based on Green's function

Abstract

This study presents an interesting method based on Picard-Ishikwa fixed point iterative method to solve nonlinear third-order boundary value problems. We develop a sequence called Picrad-Ishikawa Green’s iterative method and show that the sequence converges strongly to the fixed point of an integral operator. Our result improve many existing results in this direction.