A FAMILY OF OPTIMAL EIGHTH-ORDER ITERATIVE METHODS FOR MULTIPLE ROOTS OF NONLINEAR EQUATIONS

Oinam Thoungamba; Sunil Panday; Waikhom Henarita Chanu

doi:10.11948/20250299

2027 Volume 17 Issue 1

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Oinam Thoungamba, Sunil Panday, Waikhom Henarita Chanu. A FAMILY OF OPTIMAL EIGHTH-ORDER ITERATIVE METHODS FOR MULTIPLE ROOTS OF NONLINEAR EQUATIONS[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 54-70. doi: 10.11948/20250299

Citation:

Oinam Thoungamba, Sunil Panday, Waikhom Henarita Chanu. A FAMILY OF OPTIMAL EIGHTH-ORDER ITERATIVE METHODS FOR MULTIPLE ROOTS OF NONLINEAR EQUATIONS[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 54-70. doi: 10.11948/20250299

A FAMILY OF OPTIMAL EIGHTH-ORDER ITERATIVE METHODS FOR MULTIPLE ROOTS OF NONLINEAR EQUATIONS

1.
Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, India
2.
Department of Mathematics, Patkai Christian College (Autonomous), Patkai, Dimapur 797103, India

Author Bio: Email: sunilpanday@hotmail.co.in(S. Panday); Email: henaritawai@gmail.com(W. H. Chanu)
Corresponding author: Email: thoungambaoinam@gmail.com, thoungambaoinam@nitmanipur.ac.in(O. Thoungamba)

Abstract

Abstract

In this manuscript, we develop a family of optimal eighth-order iterative methods for approximating multiple roots of nonlinear equations with known multiplicity, derived by modifying an existing simple-root iterative method. The family is constructed by incorporating a multivariate weight function, where specific choices of this function yield distinct members while preserving eighth-order convergence. Convergence order is rigorously established through theoretical analysis. Comprehensive numerical experiments on real-life and academic problems demonstrate the accuracy and computational efficiency of the proposed methods relative to some well known existing methods. Dynamical analysis via basins of attraction in the complex plane further reveals the stability and convergence behavior of the proposed family.
- Iterative method /
- multiple roots /
- nonlinear equations /
- basins of attraction
MSC: 65Z05, 65H05, 41A25

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References

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