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On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their Dynamics

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  • Young Ik Kim
  • Young Hee Geum

Abstract

With an error corrector via principal branch of the m th root of a function-to-function ratio, we propose optimal quartic-order multiple-root finders for nonlinear equations. The relevant optimal order satisfies Kung-Traub conjecture made in 1974. Numerical experiments performed for various test equations demonstrate convergence behavior agreeing with theory and the basins of attractions for several examples are presented.

Suggested Citation

  • Young Ik Kim & Young Hee Geum, 2015. "On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their Dynamics," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-12, December.
    • Handle: RePEc:hin:jnddns:378517
    DOI: 10.1155/2015/378517
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