Integral equation has been one of the essential tools for various areas of applied mathematics. The aim of this article is to propose a simple, accurate and efficient iterative method for obtaining solutions for Fredholm integral equation systems of one dimension of the second kind. The proposed numerical method is based on orthogonal triangular functions. The orthogonal Triangular Functions (TFs) based method is first applied to transform the Fredholm system of integral equations to four coupled system of matrix algebraic equations. A finite iterative algorithm is then applied to solve this system to obtain the coefficients used to get the form of an approximate numerical solution of the unknown solution functions of the integral problems. Some examples are given to clarify the efficiency and accuracy of the method. The obtained numerical results are compared with other numerical methods and the exact solutions.
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