Authors: HASSAN MOHAMMAD, MOHAMMED YUSUF WAZIRI
Abstract: In this work, we propose a new alternative approximation based on the quasi-Newton approach for solving systems of nonlinear equations using the average of midpoint and Simpson's quadrature. Our goal is to enhance the efficiency of the method (Broyden's method) by reducing the number of iterations it takes to reach a solution. Local convergence analysis and computational results showing the relative efficiency of the proposed method are given.
Keywords: Broyden's method, superlinear convergence, quadrature formulae, predictor-corrector, nonlinear systems
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