University of Guilan Journal of Mathematical Modeling 2345-394X 12 2 2024 07 01 A compact discretization of the boundary value problems of the nonlinear Fredholm integro-differential equations 233 246 7445 10.22124/jmm.2023.24380.2184 EN Sadegh Amiri Department of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, P.O. Box: 13846-63113, Tehran, Iran Mojtaba Hajipour Department of Mathematics, Sahand University of Technology, P.O. Box: 51335-1996, Tabriz, Iran Journal Article 2023 04 23 In this paper, we propose a  fourth-order compact discretization method   for solving a second-order boundary value problem governed by the nonlinear Fredholm integro-differential equations.  Using an efficient approximate polynomial,  a  compact numerical integration method is first designed. Then by applying the derived numerical integration formulas, the original problem is converted into a nonlinear system of algebraic equations.  It is shown that the proposed method is easy to implement and has the third order of accuracy in the infinity norm. Some  numerical examples are presented to demonstrate its  approximation accuracy and computational efficiency,   as well as to compare the derived results with those  obtained in the literature. https://jmm.guilan.ac.ir/article_7445_07f69127ab50e977c18af14bfb0556f0.pdf