Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 8 2 2024 10 22 Quadrature Rules for Solving Two-Dimensional Fredholm Integral Equations of Second Kind 172 181 437 10.22128/gadm.2024.855.1116 EN Manochehr Kazemi Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran; Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran 0000-0001-8392-6690 Hamid Reza Sahebi Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran 0000-0001-8258-6719 Journal Article 2024 07 27 In this paper‎, ‎an iterative method of successive approximations based on the trapezoidal quadrature rule to solve two-dimensional Fredholm integral equations of second kind (2DFIE) is proposed‎. ‎The error estimation of the proposed method is presented‎. ‎The benefit of the method is that we do not have to solve a system of algebraic equations‎. ‎Finally‎, ‎a numerical example verify the theoretical results and show the accuracy of the method. https://ansne.du.ac.ir/article_437_8435d297360901a6efb81253375004fc.pdf