Science and Education Publishing Applied Mathematics and Physics 2 2 2014 02 28 A New Approximation Method for the Systems of Nonlinear Fredholm Integral Equations 40 48 EN Salih Yalçınbaş Department of Mathematics, Faculty of Science and Arts, Celal Bayar University, Manisa, Turkey Kübra Erdem AMP2014223 10.12691/amp-2-2-3 2014 02 17 2014 02 23 2014 02 28 In this paper, we present a new approximate method for solving systems of nonlinear Fredholm integral equation. This method is based on, first, differentiating both sides of integral equations n times and then substituting the Taylor series the unknown functions in the resulting equation and later, transforming to a matrix equation. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Taylor coefficients of the solution function. Numerical results and comparisons with the exact solution are included to demostrate the validity and applicability of the technique.