A Numerical Approach for Solving Quadratic Integral Equations of UrysohnÃ¢ÂÂs Type using Radial Basis Function
Faculty of Science, Islamic Azad University, Mashhad Branch, Mashhad, Iran
- *Corresponding Author:
- Zakieh Avazzadeh
Faculty of Science, Islamic Azad University
Mashhad Branch, Mashhad, Iran
E-mail: [email protected]
Received Date: June 02, 2012; Accepted Date: July 02, 2012; Published Date: July 05, 2012
Citation: Avazzadeh Z (2012) A Numerical Approach for Solving Quadratic Integral Equations of Urysohn’s Type using Radial Basis Functions. J Appl Computat Math 1:116. doi: 10.4172/2168-9679.1000116
Copyright: © 2012 Avazzadeh Z. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
In this paper, the numerical method to obtain the approximate solution of quadratic integral equations of Urysohn’s type is presented. This class of equations is often discussed in the different way focusing on the properties of involving functions in the integral equations. The use of radial basis functions for solving the Fredholm integral equations was offered by Makroglou  and we develop the method for solving the quadratic integral equations. In this study, the radial basis functions method with the collocation scheme to obtain the numerical solution of Fredholm and Volterra quadratic integral equations of Urysohn’s type is described. This technique plays an important role to reduce a quadratic integral equation to a system of equations. Some illustrative examples are demonstrated which confirm the efficiency, validity and applicability of the presented technique.