More efficient iterative methods than Newton's method for solving nonlinear systems

  1. Ezquerro, J.A. 1
  2. Hernández, M.A. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Llibre:
Proceedings of the Seventh International Conference on Engineering Computational Technology

Editorial: Civil-Comp Press

ISBN: 978-1-905088-40-9

Any de publicació: 2010

Tipus: Capítol de llibre

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SCOPUS: 2-s2.0-84858378519 WoS: WOS:000392420200043 GOOGLE SCHOLAR

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Resum

Newton's method (quadratic convergence) is usually the most used iterative method for solving nonlinear systems of equations. In this paper, we construct, from the modification of a third-order iterative method of Chebyshev-type, a new family of fourthorder iterative methods which is more efficient than Newton's method. We study the efficiency of the methods from the efficiency index and the computational efficiency. We also analyse the semilocal convergence of the methods and apply all the analysis to the solution of mildly nonlinear elliptic boundary value problems. © 2010 Civil-Comp Press.

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Informació de finançament

This work was supported in part by the Spanish Ministry of Science and Innovation (MTM 2008-01952/MTM) and the Riojan Autonomous Community (Colabora 2009/04).

Finançadors

  • Spanish Ministry of Science and Innovation
    • MTM 2008-01952/MTM
  • Riojan Autonomous Community (Colabora)
    • 2009/04