Efficient sixth order iterative method free from higher derivatives for nonlinear equations

Ekta Sharma, Sunil Panday

Abstract


In this paper, we proposed new iterative sixth order convergence method for solving nonlinear equations. The combination of the Taylor series and composition approach is used to derive the new method. Numerous methods have been developed by many researchers whenever the function’s second and higher order derivatives exist in the neighbourhood of the root. Computing the second and higher derivative of a function is a very cumbersome and time consuming task. In terms of low computation cost, the newly proposed method finds the best approximation to the root of non-linear equations by evaluating the function and its first derivative. The proposed method has been theoretically demonstrated to have sixth-order convergence. The proposed method has an efficiency index of 1.56. Several comparisons of the proposed method with the various existing iterative method of the same order have been performed on the number of problems. Finally, the computational results suggest that the newly proposed method is efficient compared to the well-known existing methods.


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Published: 2022-01-03

How to Cite this Article:

Ekta Sharma, Sunil Panday, Efficient sixth order iterative method free from higher derivatives for nonlinear equations, J. Math. Comput. Sci., 12 (2022), Article ID 46

Copyright © 2022 Ekta Sharma, Sunil Panday. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 

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