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Basins of Attraction for Various Steffensen-Type Methods
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| Organization: | Instituto de Matem´atica Multidisciplinar, Universitat Polit`ecnica de Val`encia |
| Organization: | Department of Mathematics, Islamic Azad University |
| Organization: | Instituto de Matem´atica Multidisciplinar, Universitat Polit`ecnica de Val`encia |
| Organization: | Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda |
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| Journal of Applied Mathematics |
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Thedynamical behavior of different Steffensen-typemethods is analyzed.We check the chaotic behaviors alongside the convergence radii (understood as the wideness of the basin of attraction) needed by Steffensen-type methods, that is, derivative-free iteration functions, to converge to a root and compare the results using different numerical tests. We will conclude that the convergence radii (and the stability) of Steffensen-typemethods are improved by increasing the convergence order.The computer programming package Mathematica provides a powerful but easy environment for all aspects of numerics. This paper puts on show one of the application of this computer algebra system in finding fixed points of iteration functions.
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