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Design and multidimensional extension of iterative methods for solving nonlinear problems

Author

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  • Artidiello, S.
  • Cordero, Alicia
  • Torregrosa, Juan R.
  • Vassileva, M.P.

Abstract

In this paper, a three-step iterative method with sixth-order local convergence for approximating the solution of a nonlinear system is presented. From Ostrowski’s scheme adding one step of Newton with ’frozen’ derivative and by using a divided difference operator we construct an iterative scheme of order six for solving nonlinear systems. The computational efficiency of the new method is compared with some known ones, obtaining good conclusions. Numerical comparisons are made with other existing methods, on standard nonlinear systems and the classical 1D-Bratu problem by transforming it in a nonlinear system by using finite differences. From this numerical examples, we confirm the theoretical results and show the performance of the presented scheme.

Suggested Citation

  • Artidiello, S. & Cordero, Alicia & Torregrosa, Juan R. & Vassileva, M.P., 2017. "Design and multidimensional extension of iterative methods for solving nonlinear problems," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 194-203.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:194-203
    DOI: 10.1016/j.amc.2016.08.034
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    References listed on IDEAS

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    1. Budzko, Dzmitry & Cordero, Alicia & Torregrosa, Juan R., 2015. "A new family of iterative methods widening areas of convergence," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 405-417.
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    Cited by:

    1. Raudys R. Capdevila & Alicia Cordero & Juan R. Torregrosa, 2019. "A New Three-Step Class of Iterative Methods for Solving Nonlinear Systems," Mathematics, MDPI, vol. 7(12), pages 1-14, December.
    2. Janak Raj Sharma & Deepak Kumar & Ioannis K. Argyros & Ángel Alberto Magreñán, 2019. "On a Bi-Parametric Family of Fourth Order Composite Newton–Jarratt Methods for Nonlinear Systems," Mathematics, MDPI, vol. 7(6), pages 1-27, May.
    3. Chun, Changbum & Neta, Beny, 2019. "Developing high order methods for the solution of systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 178-190.

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