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A family of methods for solving nonlinear equations

Author

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  • Herceg, Djordje
  • Herceg, Dragoslav

Abstract

We present a family of methods for solving nonlinear equations. Some well-known classical methods and their modifications belong to our family, for example Newton, Potra-Pták, Chebyshev, Halley and Ostrowski’s methods. Convergence analysis shows that our family contains methods of convergence order from 2 to 4. All our fourth order methods are optimal in terms of the Kung and Traub conjecture. Several examples are presented and compared.

Suggested Citation

  • Herceg, Djordje & Herceg, Dragoslav, 2015. "A family of methods for solving nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 882-895.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:882-895
    DOI: 10.1016/j.amc.2015.03.028
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    Cited by:

    1. Abro, Hameer Akhtar & Shaikh, Muhammad Mujtaba, 2019. "A new time-efficient and convergent nonlinear solver," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 516-536.

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