A Modification of Newton's Method Using Gauss-Legendre Quadrature Rules

Mohammad Masjed-Jamei,Zahra Moalemi

Keywords: Newton's Method Iterative methods Gauss-Legendre quadrature rule Order of convergence Asymptotic error constant.

Abstract: In this paper, a fourth-order modification of Newton's method, which is based on Gauss-Legendre quadrature rules, is constructed for solving nonlinear equations. The convergence analysis of the proposed method is studied and numerical examples are given to compare the efficiency of the method with respect to other known iterative methods.

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