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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 7498136, 10 pages
https://doi.org/10.1155/2017/7498136
Research Article

Application of Reproducing Kernel Hilbert Space Method for Solving a Class of Nonlinear Integral Equations

1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14515, Iran
2Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Correspondence should be addressed to M. Ali Fariborzi Araghi; moc.liamg@ihgara.izrobiraf

Received 11 November 2016; Revised 7 February 2017; Accepted 8 February 2017; Published 16 March 2017

Academic Editor: Haipeng Peng

Copyright © 2017 Sedigheh Farzaneh Javan 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.

Abstract

A new approach based on the Reproducing Kernel Hilbert Space Method is proposed to approximate the solution of the second-kind nonlinear integral equations. In this case, the Gram-Schmidt process is substituted by another process so that a satisfactory result is obtained. In this method, the solution is expressed in the form of a series. Furthermore, the convergence of the proposed technique is proved. In order to illustrate the effectiveness and efficiency of the method, four sample integral equations arising in electromagnetics are solved via the given algorithm.