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Abstrakty
The interest in efficient root-finding iterations is nowadays growing and influenced by the widespread use of high-speed computers. On the other hand, the calculation of derivatives is often hard, when the problems are formulated in terms of nonlinear equations and as a result, the importance of derivative-free methods emerges. For these reasons, some efficient three-step families of iterations for solving nonlinear equations are suggested, where the analytical proofs show their seventh-order error equations consuming only four function evaluations per iteration. We employ hard numerical test problems to illustrate the accuracy of the new methods from the families.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
163--173
Opis fizyczny
Bibliogr. 13 poz., tab.
Twórcy
autor
- Islamic Azad University, Department of Mathematics, Zahedan Branch, Zahedan, Iran, fazlollah.soleymani@gmail.com
Bibliografia
- [1] A. Iliev, N. Kyurkchiev, Nontrivial Methods in Numerical Analysis (Selected Topics in Numerical Analysis), Lambert Acad. Publishing, 2010.
- [2] S.K. Khattri, I.K. Argyros, Sixth order derivative free family of iterative methods, Appl. Math. Comput. 217 (2011), 5500-5507.
- [3] H.T. Kung, J.F. Traub, Optimal order of one-point and multipoint iteration, Journal of ACM 21 (1974), 643-651.
- [4] W. Liu, L. Wang, X. Bai, H. Zhang, Optimization calculation and analysis of moving load of the railgun by Newton method, Modern Appl. Sci. 5 (2011), 212-216.
- [5] Y. Peng, H. Feng, Q. Li, X. Zhang, A fourth-order derivative-free algorithm for nonlinear equations, J. Comput. Appl. Math. 15 (2011), 2551-2559.
- [6] H. Ren, Q. Wu, W. Bi, A class of two-step Steffensen type methods with fourth-order convergence, Appl. Math. Comput. 209 (2009), 206-210.
- [7] M. Sharifi, D.K.R. Babajee, F. Soleymani, Finding the solution of nonlinear equations by a class of optimal methods, Comput. Math. Appl. 63 (2012), 764-774.
- [8] F. Soleymani, M. Sharifi, On a cubically iterative scheme for solving nonlinear equations, Far East J. Appl. Math. 43 (2010), 137-143.
- [9] F. Soleymani, S. Karimi Vanani, Optimal Steffensen-type methods with eighth order of convergence, Comput. Math. Appl. 62 (2011), 4619-4626.
- [10] F. Soleymani, S.K. Khattri, S. Karimi Vanani, Two new classes of optimal Jarratt-type fourth-order methods, Appl. Math. Lett. 25 (2012), 847-853.
- [11] J.F. Steffensen, Remarks on iteration, Skand. Aktuarietidskr 16 (1933), 64-72.
- [12] J.F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, Inc., Engle-wood Cliffs, NJ, 1964.
- [13] Q. Ye, X. Xu, A class of Newton-like methods with cubic convergence for nonlinear equations, Fixed Point Theory 11 (2010), 161-168.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0009-0015