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A family of Kurchatov-type methods and its stability

Author

Listed:
  • Cordero, Alicia
  • Soleymani, Fazlollah
  • Torregrosa, Juan R.
  • Haghani, F. Khaksar

Abstract

We present a parametric family of iterative methods with memory for solving nonlinear equations, that includes Kurchatov’s scheme, preserving its second-order convergence. By using the tools of multidimensional real dynamics, the stability of members of this family is analyzed on low-degree polynomials, showing that some elements of this class have more stable behavior than the original Kurchatov’s method. We extend this family to multidimensional case and present different numerical tests for several members of the class on nonlinear systems. The numerical results obtained confirm the dynamical analysis made.

Suggested Citation

  • Cordero, Alicia & Soleymani, Fazlollah & Torregrosa, Juan R. & Haghani, F. Khaksar, 2017. "A family of Kurchatov-type methods and its stability," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 264-279.
    • Handle: RePEc:eee:apmaco:v:294:y:2017:i:c:p:264-279
    DOI: 10.1016/j.amc.2016.09.021
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    References listed on IDEAS

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    1. Campos, Beatriz & Cordero, Alicia & Torregrosa, Juan R. & Vindel, Pura, 2015. "A multidimensional dynamical approach to iterative methods with memory," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 701-715.
    2. Geum, Young Hee & Kim, Young Ik & Magreñán, Á. Alberto, 2016. "A biparametric extension of King’s fourth-order methods and their dynamics," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 254-275.
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    Cited by:

    1. Candela, V. & Peris, R., 2019. "A class of third order iterative Kurchatov–Steffensen (derivative free) methods for solving nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 93-104.

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