New Family of Multi-Step Iterative Methods Based on Homotopy Perturbation Technique for Solving Nonlinear Equations

Huda J. Saeed, Ali Hasan Ali, Rayene Menzer, Ana Danca Poțclean () and Himani Arora
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Huda J. Saeed: Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq
Ali Hasan Ali: Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq
Rayene Menzer: Institute of Mathematics, University of Debrecen, Pf. 400, H-4002 Debrecen, Hungary
Ana Danca Poțclean: Department of Mathematics, Technical University of Cluj-Napoca, Str. Memorandumului nr. 28, 400114 Cluj-Napoca, Romania
Himani Arora: Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, India

Mathematics, 2023, vol. 11, issue 12, 1-13

Abstract: This research aims to propose a new family of one-parameter multi-step iterative methods that combine the homotopy perturbation method with a quadrature formula for solving nonlinear equations. The proposed methods are based on a higher-order convergence scheme that allows for faster and more efficient convergence compared to existing methods. It aims also to demonstrate that the efficiency index of the proposed iterative methods can reach up to 4 3 ≈ 1.587 and 8 4 ≈ 1.681 , respectively, indicating a high degree of accuracy and efficiency in solving nonlinear equations. To evaluate the effectiveness of the suggested methods, several numerical examples including their performance are provided and compared with existing methods.

Keywords: homotopy perturbation; second derivative-free; iterative methods; nonlinear equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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