A new Householders method free from second derivatives for solving nonlinear equations and polynomiography

Volume 9, Issue 3, pp 998--1007 http://dx.doi.org/10.22436/jnsa.009.03.28

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Authors

Waqas Nazeer - Division of Science and Technology, University of Education, Lahore 54000, Pakistan. Muhmmad Tanveer - Department of Mathematics and Statistics, University of Lahore, Lahore 54000, Pakistan. Shin Min Kang - Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, Korea. Amir Naseem - Department of Mathematics, Lahore Leads University, Lahore 54810, Pakistan.

Abstract

In this paper, we describe the new Husehölder's method free from second derivatives for solving nonlinear equations. The new Husehölder's method has convergence of order five and efficiency index \(5^{\frac{1}{3}} \approx 1.70998\), which converges faster than the Newton's method, the Halley's method and the Husehölder's method. The comparison table demonstrate the faster convergence of our method. Polynomiography via the new Husehölder's method is also presented.

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Keywords

• Nonlinear equation
• Newton's method
• Halley's method
• Husehölder's method
• polynomiography.

MSC

•  65H05
•  30C10
•  30C15

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