On optimal fourth-order iterative methods free from second derivative and their dynamics. (English) Zbl 1277.65031

Chun, Changbum; Lee, Mi Young; Neta, Beny; Džunić, Jovana

Appl. Math. Comput. 218, No. 11, 6427-6438 (2012).

Summary: New fourth-order optimal root-finding methods for solving nonlinear equations are proposed. The classical Jarratt’s family of fourth-order methods is obtained as special case. We then present results which describe the conjugacy classes and dynamics of the presented optimal method for complex polynomials of degree two and three. The basins of attraction of existing optimal methods and our method are presented and compared to illustrate their performance.

MSC:

65H05

Numerical computation of solutions to single equations

Keywords:

iterative methods; order of convergence; rational maps; basin of attraction; Julia sets; conjugacy classes; numerical examples; root-finding method; nonlinear equation

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