Numerical Solution for the 2D Linear Fredholm Functional Integral Equations

Abstract

In this work, a numerical method is applied for obtaining numerical solutions of Fredholm two-dimensional functional linear integral equations based on the radial basis function (RBF). To find the approximate solutions of these types of equations, first, we approximate the unknown function as a finite series in terms of basic functions. Then, by using the proposed method, we give a formula for determining the unknown function. Using this formula, we obtain a numerical method for solving Fredholm two-dimensional functional linear integral equations. Using the proposed method, we get a system of linear algebraic equations which are solved by an iteration method. In the end, the accuracy and applicability of the proposed method are shown through some numerical applications.