A new optimal iterative algorithm for solving nonlinear equations

Dhyan R.  Gorashiya; Rajesh C.  Shah

doi:10.59400/jam.v2i1.477

A new optimal iterative algorithm for solving nonlinear equations

Dhyan R. Gorashiya Department of Metallurgical and Materials Engineering, Faculty of Technology & Engineering, The Maharaja Sayajirao University of Baroda, Vadodara 390001, Gujarat State, India http://orcid.org/0000-0001-8001-9569
Rajesh C. Shah Department of Applied Mathematics, Faculty of Technology & Engineering, The Maharaja Sayajirao University of Baroda, Vadodara 390001, Gujarat State, India

Ariticle ID: 477

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DOI: https://doi.org/10.59400/jam.v2i1.477

Keywords: iterative algorithm; second-order convergence; nonlinear equations; newton’s method; optimal method

Abstract

The aim of this paper is to propose a new iterative algorithm (scheme or method) for solving algebraic and transcendental equations, considering a fixed point and an initial guess value on the x-axis. The concepts of the slope of a line and the Taylor series are used in the derivation. The algorithm has second-order convergence and requires two function evaluations in each step, which shows that it is optimal with a computational efficiency index of 1.414 and an informational efficiency of 1. The validity of the algorithm is examined by solving some examples and their comparisons with Newton’s method.

References

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Published

2024-02-28

How to Cite

Gorashiya, D. R., & Shah, R. C. (2024). A new optimal iterative algorithm for solving nonlinear equations. Journal of AppliedMath, 2(1), 477. https://doi.org/10.59400/jam.v2i1.477

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