Article citationsMore>>

Zheng, Q., Huang, F.X., Guo, X.H. and Feng, X.L. (2013) Doubly-Accelerated Steffensens Methods with Memory and Their Applications on Solving Nonlinear ODEs. Journal of Computational Analysis and Applications, 15, 886-891.

has been cited by the following article:

• TITLE: Two Families of Multipoint Root-Solvers Using Inverse Interpolation with Memory

  AUTHORS: Zhongli Liu, Quan Zheng

  KEYWORDS: Nonlinear Equation, General Multipoint Iteration, Inverse Interpolation, Order of Convergence, Basin of Attraction

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.3, March 28, 2023

  ABSTRACT: In this paper, a general family of derivative-free n + 1-point iterative methods using n + 1 evaluations of the function and a general family of n-point iterative methods using n evaluations of the function and only one evaluation of its derivative are constructed by the inverse interpolation with the memory on the previous step for solving the simple root of a nonlinear equation. The order and order of convergence of them are proved respectively. Finally, the proposed methods and the basins of attraction are demonstrated by the numerical examples.