A family of Kurchatov-type methods and its stability

Alicia Cordero, Fazlollah Soleymani, Juan R. Torregrosa and F. Khaksar Haghani

Applied Mathematics and Computation, 2017, vol. 294, issue C, 264-279

Abstract: 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.

Keywords: Iterative methods with memory; Kurchatov’s scheme; Bifurcation diagrams; Chaos; Stability; Nonlinear systems (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:294:y:2017:i:c:p:264-279

DOI: 10.1016/j.amc.2016.09.021

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