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A Modified Newton–Özban Composition for Solving Nonlinear Systems

Rajni Sharma

Department of Applied Sciences, D. A. V. Institute of Engineering and Technology, Jalandhar 144008, Punjab, India

E-mail Address: rajni_daviet@yahoo.com

Corresponding author.

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Janak Raj Sharma

Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, Punjab, India

E-mail Address: jrshira@yahoo.co.in

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, and

Nitin Kalra

Department of Applied Sciences, D. A. V. Institute of Engineering and Technology, Jalandhar 144008, Punjab, India

I. K. Gujral Punjab Technical University, Jalandhar-Kapurthala Highway, Kapurthala 144601, Punjab, India

E-mail Address: kalranitin17@yahoo.com

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https://doi.org/10.1142/S0219876219500476Cited by:11 (Source: Crossref)

Abstract

In this work, a modified Newton–Özban composition of convergence order six for solving nonlinear systems is presented. The first two steps of proposed scheme are based on third-order method given by Özban [Özban, A. Y. [2004] “Some new variants of Newton’s method,” Appl. Math. Lett. 17, 677–682.] for solving scalar equations. Computational efficiency of the presented method is discussed and compared with well-known existing methods. Numerical examples are studied to demonstrate the accuracy of the proposed method. The basins of attraction of some of the existing methods along with the proposed method are given to exhibit their performance.

Keywords:

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