Extended convergence of a sixth order scheme for solving equations under ω–continuity conditions

[1] Amat, S. Busquier,S., Convergence and numerical analysis of two-step Steffensen’s methods, Comput. Math. Appl. 49 (2005) 13-22.10.1016/j.camwa.2005.01.002 Search in Google Scholar

[2] Amat, S. Busquier, S.,A two-step Steffensen’s under modified convergence conditions, J. Math. Anal. Appl. 324 (2006) 1084-1092.10.1016/j.jmaa.2005.12.078 Search in Google Scholar

[3] I.K. Argyros, Computational theory of iterative methods. Series: Studies in Computational Mathematics, 15, Editors: C.K.Chui and L. Wuytack, Elsevier Publ. Co. New York, U.S.A, 2007. Search in Google Scholar

[4] I.K. Argyros, S. Hilout, Weaker conditions for the convergence of Newton’s method. J. Complexity 28 (2012) 364–387.10.1016/j.jco.2011.12.003 Search in Google Scholar

[5] I. K.Argyros, A. A. Magréñan, A contemporary study of iterative methods, Elsevier (Academic Press), New York, 2018. Search in Google Scholar

[6] I. K.Argyros, A. A. Magréñan, Iterative methods and their dynamics with applications, CRC Press, New York, USA, 2017. Search in Google Scholar

[7] Argyros,I. K., George, S., Mathematical modeling for the solution of equations and systems of equations with applications, Volume-IV, Nova Publishes, NY, 2020.10.52305/EQOT3361 Search in Google Scholar

[8] Argyros,I. K., George, S., On the complexity of extending the convergence region for Traub’s method, Journal of Complexity 56 (2020) 101423, https://doi.org/10.1016/j.jco.2019.10142310.1016/j.jco.2019.101423 Search in Google Scholar

[9] Cordero, A., Hueso, J.L., Martinez, E., Torregrosa, J.R.: A modified Newton-Jarratt’s composition. Numer. Algorithms 55, 87-99 (201010.1007/s11075-009-9359-z Search in Google Scholar

[10] Jarratt, P.: Some fourth order multipoint iterative methods for solving equations. Math. Comput. 20, 434-437 (1966)10.1090/S0025-5718-66-99924-8 Search in Google Scholar

[11] Montazeri, H., Soleymani, F., Shateyi, S., Motsa, S.S.: On a new method for computing the numerical solution of systems of nonlinear equations. J. Appl. Math., 2012, Article ID 751975, 15 p, (2012)10.1155/2012/751975 Search in Google Scholar

[12] Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970) Search in Google Scholar

[13] Soleymani, F., Lofti, T., Bakhtiari, P., A multi-step class of iterative methods for nonlinear systems, Optim. Lett., 8 (2014), 1001-1015.10.1007/s11590-013-0617-6 Search in Google Scholar