An efficient two-parametric family with memory for nonlinear equations

作者：Cordero Alicia; Lotfi Taher; Bakhtiari Parisa; Torregrosa Juan R^*

来源：Numerical Algorithms, 2015, 68(2): 323-335.

DOI：10.1007/s11075-014-9846-8

• Multipoint iterative method
• Nonlinear equation
• Optimal order
• Method with memory
• Kung-Traub's conjecture

A new two-parametric family of derivative-free iterative methods for solving nonlinear equations is presented. First, a new biparametric family without memory of optimal order four is proposed. The improvement of the convergence rate of this family is obtained by using two self-accelerating parameters. These varying parameters are calculated in each iterative step employing only information from the current and the previous iteration. The corresponding R-order is 7 and the efficiency index 7(1/3) = 1.913. Numerical examples and comparison with some existing derivative-free optimal eighth-order schemes are included to confirm the theoretical results. In addition, the dynamical behavior of the designed method is analyzed and shows the stability of the scheme.

• 出版日期2015-2