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Abstract and Applied Analysis
Volume 2015, Article ID 219616, 12 pages
Research Article

On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation

1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia (UPM), Selangor, Malaysia
2Technical Institute of Alsuwerah, The Middle Technical University, Baghdad, Iraq
3Faculty of Science and Technology, Universiti Sains Islam Malaysia (USIM), Negeri Sembilan, Malaysia
4Institute for Mathematical Research, Universiti Putra Malaysia (UPM), Selangor, Malaysia
5Department of Process and Food Engineering, Faculty of Engineering, Universiti Putra Malaysia (UPM), Selangor, Malaysia

Received 19 July 2014; Accepted 6 October 2014

Academic Editor: Gaohang Yu

Copyright © 2015 Hameed Husam Hameed et al. 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.


We develop the Newton-Kantorovich method to solve the system of nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method.