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Cordero, A. and Torregrosa, J.R. (2007) Variants of Newtons Method Using Fifth-Order Quadrature Formulas. Applied Mathematics and Computation, 190, 686-698.
https://doi.org/10.1016/j.amc.2007.01.062

has been cited by the following article:

• TITLE: Gauss-Legendre Iterative Methods and Their Applications on Nonlinear Systems and BVP-ODEs

  AUTHORS: Zhongli Liu, Guoqing Sun

  KEYWORDS: Iterative Method, Gauss-Legendre Quadrature Formula, Nonlinear Systems, Third-Order Convergence, Nonlinear ODEs

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.11, November 18, 2016

  ABSTRACT: In this paper, a group of Gauss-Legendre iterative methods with cubic convergence for solving nonlinear systems are proposed. We construct the iterative schemes based on Gauss-Legendre quadrature formula. The cubic convergence and error equation are proved theoretically, and demonstrated numerically. Several numerical examples for solving the system of nonlinear equations and boundary-value problems of nonlinear ordinary differential equations (ODEs) are provided to illustrate the efficiency and performance of the suggested iterative methods.