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All Journal Journal of the Indonesian Mathematical Society Journal of Fundamental Mathematics and Applications (JFMA)
Imran, M
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Decision Sciences, Operations Research & Management Mathematics

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MODIFIED HOUSEHOLDER METHOD OF FIFTH ORDER OF CONVERGENCE AND ITS DYNAMICS ON COMPLEX PLANE Putri, Ayunda; Imran, M; Marjulisa, Rike
Journal of Fundamental Mathematics and Applications (JFMA) Vol 6, No 2 (2023)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v6i2.20554

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. Weprovide 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.
A NEW THREE- STEP DERIVATIVE FREE ITERATIVE METHOD AND ITS DYNAMICS Syamsudhuha, Syamsudhuha; Imran, M; Putri, Ayunda; Deswita, Leli; Amelia, Riski
Journal of the Indonesian Mathematical Society Vol. 30 No. 3 (2024): NOVEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.3.1533.361-373

Abstract

A new free derivative iterative method is presented in this article. The method is developed by combining Newton’s method and Euler’s method. Deriva- tives in this method are approximated by forward difference, hyperbola and divided difference. The order of convergence is proven analytically to be of sixth order. Numerical results exhibit that the new method is comparable to other methods. Basins of attraction are also provided to support the proposed method.
Co-Authors Ayunda Putri Leli Deswita Rike Marjulisa Riski Amelia, Riski Syamsudhuha Syamsudhuha