Basins of Attraction for Various Steffensen-Type Methods
Keyword(s):
The dynamical behavior of different Steffensen-type methods 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-type methods are improved by increasing the convergence order. The computer programming package MATHEMATICAprovides 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.
1998 ◽
Vol 01
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pp. 161-180
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2020 ◽
Vol 30
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pp. 2050072
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pp. 1750118
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2016 ◽
Vol 374
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pp. 20150205
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