# Application Of Multipoint Secant-Type Method ForFinding Roots 0f Nonlinear Equations

## Authors

• R. Thukral Padé Research Centre, 39 Deanswood Hill, Leeds, West Yorkshire, LS17 5JS, England

## Keywords:

Order of convergence, Root-finding, Nonlinear algebraic equations, Simple root, Secant-type methods

## Abstract

In this paper, we introduce a family of pk-order iterative schemes for finding the simple root of a nonlinear algebraic equation of the function fx=0 by using the divided difference approximation. The proposed method uses one evaluation of the function per iteration and can achieve convergence order pk. The error equation and asymptotic convergence constant are proved theoretically and numerically. Numerical examples are included to demonstrate the exceptional convergence speed of the proposed method and thus verify the theoretical results

## References

M. Baccouch, A family of higher order numerical methods for solving nonlinear algebraic equations with simple and multiple roots, Int. J. Appl. Comput.Math., 3 (2017) 1119-1133. https://doi.org/10.1007/s40819-017-0405-6

A. M. Ostrowski, Solutions of equations and system of equations, Academic Press, New York, 1960.

M. S. Petkovic, B. Neta, L. D. Petkovic, J. Dzunic, Multipoint methods for solving nonlinear equations, Elsevier 2012.

A. Sidi. Generalization of the secant method for nonlinear equations. Appl. Math. E-Notes, 8:115–123, 2008.

A. Sidi. Application of a Generalized secant method to nonlinear equations with complex roots., Axioms 10 (2021) 169, 1-11. https://doi.org/10.3390/axioms10030169

R. Thukral, A new secant-type method for solving nonlinear equations, Amer. J. Comput. Appl. Math. 8 (2) (2018) 32-36. doi:10.5923/j.ajcam.20180802.02

R. Thukral, Further development of secant-type methods for solving nonlinear equations, Inter. J. Adv. Math. 38 (5) (2018) 45-53.

R. Thukral, New three-point secant-type methods for solving nonlinear equations, Amer. J. Comput. Appl. Math. 10 (1) (2020) 15-20. doi:10.5923/j.ajcam.20201001.03

R. Thukral, Further improvement of secant-type methods for solving nonlinear equations, Amer. J. Comput. Appl. Math. 11 (3) (2021) 60-64. doi:10.5923/j.ajcam.20211103.02

R. Thukral, New variants of the secant-type method for finding roots of nonlinear equations, Amer. J. Comput. Appl. Math. 13 (2) (2023) 45-49. doi:10.5923/j.ajcam.20231302.03

J. F. Traub, Iterative Methods for solution of equations, Chelsea publishing company, New York 1977. https://doi.org/10.1017/S0008439500028125

S. Weerakoon, T. G. I. Fernando, A variant of Newton’s method with accelerated third-order convergence, Appl. Math. Lett. 13 (2000) 87-93. https://doi.org/10.1016/S0893-9659(00)00100-2

2024-02-22

## How to Cite

Thukral, R. . (2024). Application Of Multipoint Secant-Type Method ForFinding Roots 0f Nonlinear Equations. JOURNAL OF ADVANCES IN MATHEMATICS, 23, 61–69. https://doi.org/10.24297/jam.v23i.9588

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