Generalized Iteration Method via Green's Function for the Solution of the Fourth-order Boundary Value Problems

  • Fatma Aydın Akgün Yildiz Technical University
  • Zaur Rasulov Yildiz Technical University
Keywords: Boundary value problems, iteration method, Green's function, integral operator, rate of convergence


The aim of this paper is to extend and generalize Picard-Green’s fixed point iteration method for the solution of fourth-order Boundary Value Problems. Several numerical applications to linear and nonlinear fourth-order Boundary Value Problems are discussed to illustrate the main results.

Author Biography

Fatma Aydın Akgün, Yildiz Technical University

F. Aydin Akgun received
her Ph.D. in Istanbul, Turkiye
from Yildiz Technical University
in 2008. Her thesis was on
boundary value problems. Several
papers on boundary value
problems were published from
1999 - 2009. In 2010 she went
to Indiana University, in America,
to work with Professor Rhoades
on summability and Hausdorff
matrices. Several papers on summability have recently been
published. She is Assoc. Prof. in Department of Mathematical Engineering in Yildiz Technical University.

Nonlinear Analysis