応用および計算数学ジャーナル

A Numerical Approach for Solving Quadratic Integral Equations of Urysohn’s Type using Radial Basis Function

Abstract

Zakieh Avazzadeh

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 [1] 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.