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A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order

Author

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  • F. Soleymani
  • S. Karimi Vanani
  • M. Jamali Paghaleh

Abstract

A class of three-step eighth-order root solvers is constructed in this study. Our aim is fulfilled by using an interpolatory rational function in the third step of a three-step cycle. Each method of the class reaches the optimal efficiency index according to the Kung-Traub conjecture concerning multipoint iterative methods without memory. Moreover, the class is free from derivative calculation per full iteration, which is important in engineering problems. One method of the class is established analytically. To test the derived methods from the class, we apply them to a lot of nonlinear scalar equations. Numerical examples suggest that the novel class of derivative-free methods is better than the existing methods of the same type in the literature.

Suggested Citation

  • F. Soleymani & S. Karimi Vanani & M. Jamali Paghaleh, 2012. "A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, February.
    • Handle: RePEc:hin:jnljam:568740
    DOI: 10.1155/2012/568740
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    Cited by:

    1. Jian Li & Xiaomeng Wang & Kalyanasundaram Madhu, 2019. "Higher-Order Derivative-Free Iterative Methods for Solving Nonlinear Equations and Their Basins of Attraction," Mathematics, MDPI, vol. 7(11), pages 1-15, November.
    2. F. Soleymani, 2012. "Optimized Steffensen-Type Methods with Eighth-Order Convergence and High Efficiency Index," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-18, September.

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