DOI: https://doi.org/10.14710/jfma.v6i2.20554

MODIFIED HOUSEHOLDER METHOD OF FIFTH ORDER OF CONVERGENCE AND ITS DYNAMICS ON COMPLEX PLANE

*Ayunda Putri orcid  -  Department of Mathematics, Universitas Riau, Jl. Bina Widya, Tampan, Pekanbaru, Indonesia 28293, Indonesia
M Imran scopus  -  Department of Mathematics, Universitas Riau, Jl. Bina Widya, Tampan, Pekanbaru, Indonesia 28293, Indonesia
Rike Marjulisa orcid  -  Department of Mathematics, Universitas Riau, Jl. Bina Widya, Tampan, Pekanbaru, Indonesia 28293, Indonesia

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Abstract

In this paper, a modified Householder method of fifth order is proposed for solving nonlinear equations. The modification is done by adapting a cubic interpolation polynomial to approximate the second derivative in the Householder method. We
provide a theorem to prove the order of convergence of the proposed method. The simulations reveal that the proposed method needs fewer iterations, even with challenging initial guesses, and excels in sending a large portion of initial points to convergence and exhibits rapid convergence.

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Keywords: Iterative methods, Househ"older method, order of convergence, basins of attraction

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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