A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics

Young Hee Geum, Young Ik Kim and Beny Neta

Applied Mathematics and Computation, 2015, vol. 270, issue C, 387-400

Abstract: Under the assumption of the known multiplicity of zeros of nonlinear equations, a class of two-point sextic-order multiple-zero finders and their dynamics are investigated in this paper by means of extensive analysis of modified double-Newton type of methods. With the introduction of a bivariate weight function dependent on function-to-function and derivative-to-derivative ratios, higher-order convergence is obtained. Additional investigation is carried out for extraneous fixed points of the iterative maps associated with the proposed methods along with a comparison with typically selected cases. Through a variety of test equations, numerical experiments strongly support the theory developed in this paper. In addition, relevant dynamics of the proposed methods is successfully explored for various polynomials with a number of illustrative basins of attraction.

Keywords: Multiple-zero finder; Extraneous fixed point; Double-Newton; Basins of attraction (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (14)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:270:y:2015:i:c:p:387-400

DOI: 10.1016/j.amc.2015.08.039

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