Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8771A Local and Semilocal Convergence of the Continuous Analogy of Newton's MethodZhanlavT; National University of Mongolia Ulan-Batorzhanlav@yahoo.comChuluunbaatarO; Joint Institute for Nuclear Researchchuka@jinr.ruNational University of Mongolia Ulan-BatorJoint Institute for Nuclear Research150120121344308092016Copyright © 2012,2012In this paper, a region of convergence of the continuous analogy of Newton's method is defined and an optimal choice of the parameter t is proposed. For the damped Newton's method a global convergence is proved and error bounds are obtained. The damping strategies allow one to extend the convergence domain of the initial guesses. Several damping strategies were compared. Numerical examples are given and confirm the theoretical results.nonlinear equations in Banach spacesdamped Newton's methodrecurrence relationserror boundsнелинейные уравнения в банаховых пространствахзатухающий метод Ньютонарекуррентные соотношенияоценка погрешности