A family of Kurchatov-type methods and its stability

作者：Cordero Alicia; Soleymani Fazlollah; Torregrosa Juan R^*; Haghani F Khaksar

来源：Applied Mathematics and Computation, 2017, 294: 264-279.

DOI：10.1016/j.amc.2016.09.021

• Iterative methods with memory
• Kurchatov's scheme
• Bifurcation diagrams
• Chaos
• Stability
• Nonlinear systems

We present a parametric family of iterative methods with memory for solving nonlinear equations, that includes Kurchatov's scheme, preserving its second-order convergence. By using the tools of multidimensional real dynamics, the stability of members of this family is analyzed on low-degree polynomials, showing that some elements of this class have more stable behavior than the original Kurchatov's method. We extend this family to multidimensional case and present different numerical tests for several members of the class on nonlinear systems. The numerical results obtained confirm the dynamical analysis made.

• 出版日期2017-2-1