A local and a semi-local convergence analysis are presented for the Kurchatov-type method to solve numerically nonlinear equations in a Banach space. The method depends on a real parameter. By specializing the parameter, we obtain methods already stu...
The technique of using the restricted convergence region is applied to study a semilocal convergence of the Newton–Kurchatov method. The analysis is provided under weak conditions for the derivatives and the first order divided differences. Con...
Two novel Kurchatov-type first-order divided difference operators were designed, which were used for constructing the variable parameter of three derivative-free iterative methods. The convergence orders of the new derivative-free methods are 3, (5+1...
Some Kurchatov-type accelerating parameters are used to construct some derivative-free iterative methods with memory for solving nonlinear systems. New iterative methods are developed from an initial scheme without memory with order of convergence th...
The study of the microworld, quantum physics including the fundamental standard models are closely related to the basis of symmetry principles. These phenomena are reduced to solving nonlinear equations in suitable abstract spaces. Such equations are...
We present a local convergence of the combined Newton-Kurchatov method for solving Banach space valued equations. The convergence criteria involve derivatives until the second and Lipschitz-type conditions are satisfied, as well as a new center-Lipsc...
Solving equations in abstract spaces is important since many problems from diverse disciplines require it. The solutions of these equations cannot be obtained in a form closed. That difficulty forces us to develop ever improving iterative methods. In...
The dynamical analysis of Kurchatov’s scheme is extended to Traub’s method. The difference here is that Traub’s method requires two additional starting points. Therefore, the map is three-dimensional instead of 2-D. We obtain a comp...
This paper analyzes the results of studies carried out at the National Research Center “Kurchatov Institute”, Moscow, using the methods of neutron and X-ray synchrotron tomography from the point of view of the preservation state of metal objects. Obj...
Some iterative schemes with memory were designed for approximating the inverse of a nonsingular square complex matrix and the Moore–Penrose inverse of a singular square matrix or an arbitrary m×n complex matrix. A Kurchatov-type scheme an...
A local and semi-local convergence is developed of a class of iterative methods without derivatives for solving nonlinear Banach space valued operator equations under the classical Lipschitz conditions for first-order divided differences. Special cas...
We used a Kurchatov-type accelerator to construct an iterative method with memory for solving nonlinear systems, with sixth-order convergence. It was developed from an initial scheme without memory, with order of convergence four. There exist few mul...
Almost all experimental studies of the characteristics of nuclear-excited plasma formed by excitation of gaseous media with nuclear reactions products are conducted at pulsed nuclear reactors that differ in the composition and design of the core, the...
The results of the research of a composite based on multi-walled carbon nanotubes (MWCNTs) decorated with CuO/Cu2O/Cu nanoparticles deposited by the cupric formate pyrolysis are discussed. The study used a complementary set of methods, including scan...
A review of experimental studies carried out at the NRC “Kurchatov Institute” on plasma-facing thermonuclear fusion reactor materials is presented in the paper. An experimental method was developed to produce high-level radiation damage in materials...
The paper is devoted to the synthesis, comparison, and optimization of robust LMI-control systems for the vertical plasma position in a D-shaped tokamak, specifically the T-15MD tokamak (Kurchatov Institute, Moscow, Russia). The novelty of this work...