Abstract
We present a local convergence analysis of a two-step and derivative-free Kung–Traub’s method, which is based on a parameter and has fourth order of convergence. Using basins of attraction of the method, dynamical behavior of the scheme is studied and the best choice of the parameter is found in the sense of reliability and stability. Some illustrative examples show that as the parameter gets close to zero, radius of convergence of the method becomes larger.
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The authors express their sincere thanks to the referee’s comments which lead to the improvement of this work.
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Communicated by Joerg Fliege.
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Veiseh, H., Lotfi, T. & Allahviranloo, T. A study on the local convergence and dynamics of the two-step and derivative-free Kung–Traub’s method. Comp. Appl. Math. 37, 2428–2444 (2018). https://doi.org/10.1007/s40314-017-0458-5
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DOI: https://doi.org/10.1007/s40314-017-0458-5