A NOTE ON "A SIXTH ORDER METHOD FOR SOLVING NONLINEAR EQUATIONS"
الموضوعات : فصلنامه ریاضی
Paria Assari
1
(ORCID iD Islamic Azad University, Hamedan Branch
Iran, Islamic Republic of)
Taher Lotfi
2
(Islamic Azad University, Hamedan Branch
Iran, Islamic Republic of)
الکلمات المفتاحية: Nonlinear equation, Multi-point method, Convergence order, optimal method,
ملخص المقالة :
In this study, we modify an iterative non-optimal without memory method, in such a way that is becomes optimal. Therefore, we obtain convergence order eight with the some functional evaluations. To justify our proposed method, some numerical examples are given.
Cordero. A, Lotfi. T, Bakhtiari. P and Torregrosa. J. R, An efficient two-parametric family with memory for nonlinear equations, Numer Algor. DOI 10.1007/s11075-014-9846-8.
Cordero. A, Lotfi. T, Mahdiani. K and Torregrosa. J. R, Two optimal general classes of iterative methods with eighth-Order, Acta Appl Math. DOI 10.1007/s10440-014-9869-0.
Cordero. A, Lotfi. T, Torregrosa. J. R, Assari. P and Mahdiani. K, Some new bi-accelerator two-point methods for solving nonlinear equations, Comp. Appl. Math. DOI 10.1007/s40314-014-0192-1.
Kung. H.T and Traub. J. F, Optimal order of one-point and multipoint iteration, J. Assoc. Comput. Math. 21 (1974) 634-651.
Lotfi. T and Assari. P, A new calss of two step methods with memory for solving nonlinear equation with high efficiency index, International Journal of Mathematical Modelling and Computations. 4 (2014) 277-288.
Lotfi. T, Magrenan. A. A, Mahdiani. K and Rainer. J. J, A variant of Steffensen–King’s type family with accelerated sixth-order convergence and high efficiency index: Dynamic study and approach, Applied Mathematics and Computation. 252 (2015) 347–353.
Lotfi. T, Soleymani. F, Shateyi. S, Assari. P and Khaksar Haghani. F, New mono- and biaccelerator iterative methods with memory for nonlinear equations, Abstract and Applied Analysis. Volume 2014, Article ID 705674, 8 pages.
Lotfi. T and Tavakoli. E, On construction a new efficient Steffensen-like iterative class by applying a suitable self-accelerator parameter.
Mirzaee. F and Hamzeh. A, A sixth order method for solving nonlinear equations, International Journal of
Mathematical Modelling and Computations. 4 (2014) 55-60.
Ostrowski. A. M, Solution of Equations and Systems of Equations, Academic Press, New York, 1960.
Traub. J. F, Iterative Methods for the Solution of Equations, Prentice Hall, New York, 1964.
Weerakoon. S and Fernando. T. G. I, A variant of Newton's method with accelerated third-order convergence, J. Appl. Math. Lett. 13 (8) (2000) 87-93.
