Convergence of the two-step combined method and uniqueness of the solution of nonlinear operator equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:261

Article

Shakhno, S. M.

关键词: Nonlinear equation;    Iterative process;    The convergence order;    Radius of convergence;    Nondifferentiable operator;    Generalized Lipschitz condition;   

DOI  :  10.1016/j.cam.2013.11.018

来源: Elsevier

【 摘 要 】

Local convergence of the two-step differential-difference method for solving nonlinear operator equations for generalized Lipschitz conditions for Frechet derivatives of the first and second order and divided differences of the first order has been proven. There have been found estimations of the convergence ball's radii of this method and the uniqueness ball of solution of nonlinear equations. There has been established the superquadratical order of the convergence of the two-step combined method and a comparison of the results with the known ones has been made. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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