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A new family of iterative methods widening areas of convergence

Author

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  • Budzko, Dzmitry
  • Cordero, Alicia
  • Torregrosa, Juan R.

Abstract

A new parametric class of third-order iterative methods for solving nonlinear equations and systems is presented. These schemes are showed to be more stable than Newton’, Traub’ or Ostrowski’s procedures (in some specific cases), and it has been proved that the set of starting points that converge to the roots of different nonlinear functions is wider than the one of those respective methods. Moreover, the numerical efficiency has been checked through different numerical tests.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:252:y:2015:i:c:p:405-417
    DOI: 10.1016/j.amc.2014.12.028
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    Citations

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    Cited by:

    1. Cristina Amorós & Ioannis K. Argyros & Ruben González & Á. Alberto Magreñán & Lara Orcos & Íñigo Sarría, 2019. "Study of a High Order Family: Local Convergence and Dynamics," Mathematics, MDPI, vol. 7(3), pages 1-14, February.
    2. Ioannis K. Argyros & Ángel Alberto Magreñán & Alejandro Moysi & Íñigo Sarría & Juan Antonio Sicilia Montalvo, 2020. "Study of Local Convergence and Dynamics of a King-Like Two-Step Method with Applications," Mathematics, MDPI, vol. 8(7), pages 1-12, July.
    3. 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.
    4. Mudassir Shams & Bruno Carpentieri, 2024. "A High-Order Numerical Scheme for Efficiently Solving Nonlinear Vectorial Problems in Engineering Applications," Mathematics, MDPI, vol. 12(15), pages 1-33, July.

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