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

Introduction Quadratic integral equations provide an important tool for modeling the numerous problems in engineering and science. These equations appear in the modeling of radiative transfer, kinetic theory of gases, traffic theory, neutron transport and in many other phenomena [2-7]. So, it is clear that solving this class of integral equations can be used to describe many events in the real world. Recently, many different types of research have been focusing on the effective properties of quadratic integral equations such as existence, uniqueness, monotonic solutions and positive solutions of this class of equations [8-13]. There are a few numerical and analytical methods to estimate the solution of the quadratic integral equations such as Picard and Adomian decomposition method (ADM) [14], and some other methods [15]. In this study, the radial basis functions method with the collocation scheme for solving quadratic integral equations of Urysohn’s type is described. The use of radial basis functions for solving the Fredholm integral equation was offered by Makroglou [1] and Alipanah and Dehghan [16] facilitated this method with the quadrature integration technique. Also, this method is compared with the method via orthogonal polynomials [17]. We utilize the method for solving the quadratic integral equations. A nonlinear Fredholm quadratic integral equation of Urysohn’s type can be considered as the following general form