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Submitted
September 18, 2023
Accepted
September 11, 2024
Published
September 23, 2024
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Abstract




A new free derivative iterative method is presented in this article. The method is developed by combining Newton’s method and Euler’s method. Deriva- tives in this method are approximated by forward difference, hyperbola and divided difference. The order of convergence is proven analytically to be of sixth order. Numerical results exhibit that the new method is comparable to other methods. Basins of attraction are also provided to support the proposed method.




Keywords

forward difference divided difference efficiency index derivative-free method order of convergence basins of attraction

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite
Syamsudhuha, S., Imran, M., Putri, A., Deswita, L., & Amelia, R. (2024). A NEW THREE- STEP DERIVATIVE FREE ITERATIVE METHOD AND ITS DYNAMICS. Journal of the Indonesian Mathematical Society, 30(3). Retrieved from http://jims-a.org./index.php/jimsa/article/view/1533
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