2 research outputs found

    Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior

    Full text link
    In this paper, we present a family of optimal, in the sense of Kung-Traub's conjecture, iterative methods for solving nonlinear equations with eighth-order convergence. Our methods are based on Chun's fourth-order method. We use the Ostrowski's efficiency index and several numerical tests in order to compare the new methods with other known eighth-order ones. We also extend this comparison to the dynamical study of the different methodsThis research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 and by the Center of Excellence for Mathematics, University of Shahrekord, Iran.Cordero Barbero, A.; Fardi, M.; Ghasemi, M.; Torregrosa Sánchez, JR. (2014). Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior. Calcolo. 51(1):17-30. https://doi.org/10.1007/s10092-012-0073-11730511Bi, W., Ren, H., Wu, Q.: Three-step iterative methods with eighth-order convergence for solving nonlinear equations. J. Comput. Appl. Math. 255, 105–112 (2009)Blanchard, P.: Complex analytic dynamics on the Riemann sphere. Bull. Am. Math. Soc. 11(1), 85–141 (1984)Chun, C.: Some variants of Kings fourth-order family of methods for nonlinear equations. Appl. Math. Comput. 190, 57–62 (2007)Cordero, A., Hueso, J.L., Martínez, E., Torregrosa, J.R.: New modifications of Potra-Pták’s method with optimal fourth and eighth order of convergence. J. Comput. Appl. Math. 234, 2969–2976 (2010)Cordero, A., Torregrosa, J.R.: Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Comput. 190, 686–698 (2007)Cordero, A., Torregrosa, J.R., Vassileva, M.P.: A family of modified Ostrowski’s method with optimal eighth order of convergence. Appl. Math. Lett. 24(12), 2082–2086 (2011)Douady, A., Hubbard, J.H.: On the dynamics of polynomials-like mappings. Ann. Sci. Ec. Norm. Sup. (Paris) 18, 287–343 (1985)Kung, H.T., Traub, J.F.: Optimal order of one-point and multi-point iteration. J. Assoc. Comput. Mach. 21, 643–651 (1974)Liu, L., Wang, X.: Eighth-order methods with high efficiency index for solving nonlinear equations. Appl. Math. Comput. 215, 3449–3454 (2010)Ostrowski, A.M.: Solutions of equations and systems of equations. Academic Press, New York (1966)Sharma, J.R., Sharma, R.: A family of modified Ostrowski’s methods with accelerated eighth order convergence. Numer. Algoritms 54, 445–458 (2010)Soleymani, F., Karimi Banani, S., Khan, M., Sharifi, M.: Some modifications of King’s family with optimal eighth order of convergence. Math. Comput. Model. 55, 1373–1380 (2012)Thukral, R., Petkovic, M.S.: A family of three-point methods of optimal order for solving nonlinear equations. J. Comput. Appl. Math. 233, 2278–2284 (2010

    Design, Analysis, and Applications of Iterative Methods for Solving Nonlinear Systems

    Get PDF
    In this chapter, we present an overview of some multipoint iterative methods for solving nonlinear systems obtained by using different techniques such as composition of known methods, weight function procedure, and pseudo-composition, etc. The dynamical study of these iterative schemes provides us valuable information about their stability and reliability. A numerical test on a specific problem coming from chemistry is performed to compare the described methods with classical ones and to confirm the theoretical results
    corecore