Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan
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Received: 12 December 2018 / Revised: 20 January 2019 / Accepted: 22 January 2019 / Published: 12 February 2019
Finding a simple root for a nonlinear equation
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.
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Junjua, M.-U.-D.; Zafar, F.; Yasmin, N. Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation. Mathematics 2019, 7, 164.
Junjua M-U-D, Zafar F, Yasmin N. Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation. Mathematics. 2019; 7(2):164.
Junjua, Moin-ud-Din; Zafar, Fiza; Yasmin, Nusrat. 2019. "Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation." Mathematics 7, no. 2: 164.
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