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

Young Ik Kim and Young Hee Geum

Discrete Dynamics in Nature and Society, 2015, vol. 2015, 1-12

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.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:378517

DOI: 10.1155/2015/378517

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