International Journal of Differential Equations
Volume 2011 (2011), Article ID 989065, 10 pages
http://dx.doi.org/10.1155/2011/989065
Research Article

Convergence of the New Iterative Method

Sachin Bhalekar1 and Varsha Daftardar-Gejji2

1Department of Mathematics, Shivaji University, Kolhapur 416004, India
2Department of Mathematics, University of Pune, Pune 411007, India

Received 7 May 2011; Accepted 21 August 2011

Academic Editor: Dexing Kong

Copyright © 2011 Sachin Bhalekar and Varsha Daftardar-Gejji. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new iterative method introduced by Daftardar-Gejji and Jafari (2006) (DJ Method) is an efficient technique to solve nonlinear functional equations. In the present paper, sufficiency conditions for convergence of DJM have been presented. Further equivalence of DJM and Adomian decomposition method is established.