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Weerakoon, S. and Fernando, T.G.I. (2000) A Variant of Newton’s Method with Accelerated Third-Order Convergence. Applied Mathematics Letters, 13, 87-93.
http://dx.doi.org/10.1016/S0893-9659(00)00100-2

has been cited by the following article:

• TITLE: A New Newton-Type Method with Third-Order for Solving Systems of Nonlinear Equations

  AUTHORS: Zhongli Liu, Quanyou Fang

  KEYWORDS: Newton-Type Method, Systems of Nonlinear Equations, Third-Order Convergence, Integral Interpolation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.3 No.10, October 28, 2015

  ABSTRACT: In this paper, a new two-step Newton-type method with third-order convergence for solving systems of nonlinear equations is proposed. We construct the new method based on the integral interpolation of Newton’s method. Its cubic convergence and error equation are proved theoretically, and demonstrated numerically. Its application to systems of nonlinear equations and boundary-value problems of nonlinear ODEs are shown as well in the numerical examples.