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Volume 7
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10.3390/math7020164
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Article

Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation

by
Moin-ud-Din Junjua
*,
Fiza Zafar
and
Nusrat Yasmin
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(2), 164; https://doi.org/10.3390/math7020164
Submission received: 12 December 2018 / Revised: 20 January 2019 / Accepted: 22 January 2019 / Published: 12 February 2019
(This article belongs to the Section E1: Mathematics and Computer Science)
Versions Notes

Abstract

Finding a simple root for a nonlinear equation f ( x ) = 0 , f : I ⊆ R → R has always been of much interest due to its wide applications in many fields of science and engineering. Newton’s method is usually applied to solve this kind of problems. In this paper, for such problems, we present a family of optimal derivative-free root finding methods of arbitrary high order based on inverse interpolation and modify it by using a transformation of first order derivative. Convergence analysis of the modified methods confirms that the optimal order of convergence is preserved according to the Kung-Traub conjecture. To examine the effectiveness and significance of the newly developed methods numerically, several nonlinear equations including the van der Waals equation are tested.
Keywords: nonlinear equations; simple roots; inverse interpolation; optimal iterative methods; higher order of convergence nonlinear equations; simple roots; inverse interpolation; optimal iterative methods; higher order of convergence

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MDPI and ACS Style

Junjua, M.-u.-D.; Zafar, F.; Yasmin, N. Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation. Mathematics 2019, 7, 164. https://doi.org/10.3390/math7020164

AMA Style

Junjua M-u-D, Zafar F, Yasmin N. Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation. Mathematics. 2019; 7(2):164. https://doi.org/10.3390/math7020164

Chicago/Turabian Style

Junjua, Moin-ud-Din, Fiza Zafar, and Nusrat Yasmin. 2019. "Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation" Mathematics 7, no. 2: 164. https://doi.org/10.3390/math7020164

APA Style

Junjua, M.-u.-D., Zafar, F., & Yasmin, N. (2019). Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation. Mathematics, 7(2), 164. https://doi.org/10.3390/math7020164

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