Efficient Four-Parametric with-and-without-Memory Iterative Methods Possessing High Efficiency Indices
2018 ◽
Vol 2018
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pp. 1-12
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Keyword(s):
We construct a family of derivative-free optimal iterative methods without memory to approximate a simple zero of a nonlinear function. Error analysis demonstrates that the without-memory class has eighth-order convergence and is extendable to with-memory class. The extension of new family to the with-memory one is also presented which attains the convergence order 15.5156 and a very high efficiency index 15.51561/4≈1.9847. Some particular schemes of the with-memory family are also described. Numerical examples and some dynamical aspects of the new schemes are given to support theoretical results.
2014 ◽
Vol 2014
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pp. 1-9
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2014 ◽
Vol 2014
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pp. 1-6
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Keyword(s):
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