Abstract
Abstract. This paper presents a novel approach for solving nonlinear integral equations of Fredholm and Volterra types using a multi-layer neural network (MLNN) trained through unrestricted optimization. The learning process involves minimizing the integral equation error function using the Nelder-Mead simplex method (NMSM), enabling efficient convergence in both Fredholm and Volterra equations. Our method ensures high accuracy despite potentially time-consuming computations for complex problems, maintaining convergence and approximation precision. Furthermore, the proposed approach demonstrates robustness against high-dimensional and variant equations. Numerical experiments employing the NMSM showcase its superior performance compared to existing methods. This research offers a promising avenue for solving a system of nonlinear integral equations efficiently and accurately, with broad applicability across diverse domains.
Published Version
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