Basins of attraction for Zhou–Chen–Song fourth order family of methods for multiple roots

S. Amat, S. Busquier, S. Plaza, Iterative root-finding methods, 2004, unpublished manuscript.

Amat, 2004, Review of some iterative root-finding methods from a dynamical point of view, Sci. Ser. A Math. Sci., 10, 3

Amat, 2004, Dynamics of a family of third-order iterative methods that do not require using second derivatives, Appl. Math. Comput., 154, 735

Amat, 2005, Dynamics of the King and Jarratt iterations, Aeq. Math., 69, 212, 10.1007/s00010-004-2733-y

Chun, 2012, On optimal fourth-order iterative methods free from second derivative and their dynamics, Appl. Math. Comput., 218, 6427

Dong, 1982, A basic theorem of constructing an iterative formula of the higher order for computing multiple roots of an equation, Math. Numer. Sinica, 11, 445

Dong, 1987, A family of multipoint iterative functions for finding multiple roots of equations, Int. J. Comput. Math., 21, 363, 10.1080/00207168708803576

Hansen, 1977, A family of root finding methods, Numer. Math., 27, 257, 10.1007/BF01396176

Kung, 1974, Optimal order of one-point and multipoint iteration, J. ACM, 21, 643, 10.1145/321850.321860

Li, 2010, Some fourth-order nonlinear solvers with closed formulae for multiple roots, Comput. Math. Appl., 59, 126, 10.1016/j.camwa.2009.08.066

Liu, 2013, A new family of fourth-order methods for multiple roots of nonlinear equations, Nonlinear Anal. Model. Control, 18, 143, 10.15388/NA.18.2.14018

B. Neta, Numerical methods for the solution of equations, Net-A-Sof, 1983.

Neta, 2008, New third order nonlinear solvers for multiple roots, Appl. Math. Comput., 202, 162

Neta, 2010, Extension of Murakami’s high order nonlinear solver to multiple roots, Int. J. Comput. Math., 8, 1023, 10.1080/00207160802272263

Neta, 2014, Basins of attraction for several optimal fourth order methods for multiple roots, Math. Comput. Simul., 103, 39, 10.1016/j.matcom.2014.03.007

Neta, 2013, On a family of Laguerre methods to find multiple roots of nonlinear equations, Appl. Math. Comput., 219, 10987

Neta, 2008, High order nonlinear solver for multiple roots, Comput. Math. Appl., 55, 2012, 10.1016/j.camwa.2007.09.001

Neta, 2012, Basin attractors for various methods for multiple roots, Appl. Math. Comput., 218, 5043

Ostrowski, 1973

Petković, 2013

Schröder, 1870, Über unendlich viele Algorithmen zur auflösung der Gleichungen, Math. Ann., 2, 317, 10.1007/BF01444024

Scott, 2011, Basin attractors for various methods, Appl. Math. Comput., 218, 2584

Stewart, 2001

Traub, 1997

Victory, 1983, A higher order method for multiple zeros of nonlinear functions, Int. J. Comput. Math., 12, 329, 10.1080/00207168208803346

Vrscay, 1988, Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions, Numer. Math., 52, 1, 10.1007/BF01401018

Werner, 1981, Iterationsverfahren höherer ordnung zur lösung nicht linearer Gleichungen, Z. Angew. Math. Mech., 61

Zhou, 2011, Constructing higher-order methods for obtaining the multiple roots of nonlinear equations, J. Comput. Appl. Math., 235, 4199, 10.1016/j.cam.2011.03.014