Abstract. An efficient algorithm is proposed for solving nonlinear Fredholm integral equations (NFIEs) using the Electromagnetic Meta-Heuristic method (EM). For using this heuristic method, we first approximate a solution for NFIE. By substitution of this solution in NFIE, we will encounter an integral to compute. If this integral be computable, then we will have a system of nonlinear of algebraic equations to solve. If we can not compute this integral because of the integrand involves some unknowns, then we choose a value for each constant and next we compute the integral. But the question have is how do we select these values to achive a good solution for the integral equations? To ensure this question we try to solve the problem by EM method. For solving the system of nonlinear equations we proposed a hybrid of the Newton-GMRES and EM methods. Some numerical examples provided to show that the proposed algorithm can find solutions of NFIEs in practical computation time.

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