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

Authors

  • Fatma Aydin Akgun Yildiz Technical University
  • Zaur Rasulov Yildiz Technical University

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i3.4020

Keywords:

Boundary value problems, iteration method, Green's function, integral operator, rate of convergence

Abstract

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 Aydin Akgun, 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.

Downloads

Published

2021-08-05

Issue

Vol. 14 No. 3: (July 2021)

Section

Nonlinear Analysis

License

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Generalized Iteration Method via Green’s Function for the Solution of the Fourth-order Boundary Value Problems. (2021). European Journal of Pure and Applied Mathematics, 14(3), 969-979. https://doi.org/10.29020/nybg.ejpam.v14i3.4020