USING ELECTROMAGNETIC META-HEURISTIC ALGORITHM FOR SOLVING NONLINEAR FREDHOLM INTEGRAL EQUATIONS

Abstract

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