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A Few Iterative Methods by Using [1, n ]-Order Padé Approximation of Function and the Improvements

Author

Listed:
  • Shengfeng Li

    (Institute of Applied Mathematics, Bengbu University, Bengbu 233030, China)

  • Xiaobin Liu

    (School of Computer Engineering, Bengbu University, Bengbu 233030, China)

  • Xiaofang Zhang

    (Institute of Applied Mathematics, Bengbu University, Bengbu 233030, China)

Abstract

In this paper, a few single-step iterative methods, including classical Newton’s method and Halley’s method, are suggested by applying [ 1 , n ] -order Padé approximation of function for finding the roots of nonlinear equations at first. In order to avoid the operation of high-order derivatives of function, we modify the presented methods with fourth-order convergence by using the approximants of the second derivative and third derivative, respectively. Thus, several modified two-step iterative methods are obtained for solving nonlinear equations, and the convergence of the variants is then analyzed that they are of the fourth-order convergence. Finally, numerical experiments are given to illustrate the practicability of the suggested variants. Henceforth, the variants with fourth-order convergence have been considered as the imperative improvements to find the roots of nonlinear equations.

Suggested Citation

  • Shengfeng Li & Xiaobin Liu & Xiaofang Zhang, 2019. "A Few Iterative Methods by Using [1, n ]-Order Padé Approximation of Function and the Improvements," Mathematics, MDPI, vol. 7(1), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:55-:d:195471
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    References listed on IDEAS

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    1. Faisal Ali & Waqas Aslam & Kashif Ali & Muhammad Adnan Anwar & Akbar Nadeem, 2018. "New Family of Iterative Methods for Solving Nonlinear Models," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-12, April.
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