Results 41 to 50 of about 11,828,995 (144)
Mathematics, 2022 There are a plethora of semi-local convergence results for Newton’s method (NM). These results rely on the Newton–Kantorovich criterion. However, this condition may not be satisfied even in the case of scalar equations.
Samundra Regmi +3 more
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The convergence theorem for fourth-order super-Halley method in weaker conditions
Journal of Inequalities and Applications, 2016 In this paper, we establish the Newton-Kantorovich convergence theorem of a fourth-order super-Halley method under weaker conditions in Banach space, which is used to solve the nonlinear equations.
Lin Zheng
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Numerical treatment of singularly perturbed unsteady Burger-Huxley equation
Frontiers in Applied Mathematics and Statistics, 2023 This article deals with the numerical treatment of a singularly perturbed unsteady Burger-Huxley equation. The equation is linearized using the Newton-Raphson-Kantorovich approximation method.
Imiru Takele Daba, Gemechis File Duressa
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The Role of a Priori Estimates in the Method of Non-local Continuation of Solution by Parameter
Известия Иркутского государственного университета: Серия "Математика", 2020 An iterative method for continuation of solutions with respect to a parameter is proposed. The nonlocal case is studied when the parameter belongs to the segment of the real axis.
N.А. Sidorov
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Semilocal Convergence Analysis for Inexact Newton Method under Weak Condition
Abstract and Applied Analysis, 2012 Under the hypothesis that the first derivative satisfies some kind of weak Lipschitz conditions, a new semilocal convergence theorem for inexact Newton method is presented.
Xiubin Xu, Yuan Xiao, Tao Liu
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PROJECTION-ITERATION REALIZATION OF A NEWTON-LIKE METHOD FOR SOLVING NONLINEAR OPERATOR EQUATIONS
Journal of Optimization, Differential Equations and Their Applications, 2019 We consider the problem of existence and location of a solution of a nonlinear operator equation with a Fr´echet differentiable operator in a Banach space and present the convergence results for a projection-iteration method based on a Newton-like method
Liudmyla L. Hart
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New and Generalized Convergence Conditions for the Newton-Kantorovich Method [PDF]
Journal of Applied Analysis, 2003 For a nonlinear operator equation on a Banach space a semilocal convergence theorem for Newton's method is proved using a majorant principle. This is shown to provide some weakening of the usual results based on Lipschitz conditions. Few connections are made to the literature on other related work involving majorization techniques.
openaire +2 more sources
Mathematics, 2020 The evolutionary integral dynamical models of storage systems are addressed. Such models are based on systems of weakly regular nonlinear Volterra integral equations with piecewise smooth kernels. These equations can have non-unique solutions that depend
Denis Sidorov +4 more
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Approximate solution of a nonlinear system of integral equations using modified Newton-Kantorovich method [PDF]
, 2010 Modified Newton-Kantorovich method is developed to obtain an approximate solution for a system of nonlinear integral equations. The system of nonlinear integral equations is reduced to find the roots of nonlinear integral operator.
Ahmedov, Anvarjon +3 more
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Convergence Theorem for a Family of New Modified Halley’s Method in Banach Space
Journal of Applied Mathematics, 2014 We establish convergence theorems of Newton-Kantorovich type for a family of new modified Halley’s method in Banach space to solve nonlinear operator equations. We present the corresponding error estimate.
Rongfei Lin +3 more
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