Some quadrature-based versions of the generalized Newton method for solving nonsmooth equations

Inexact Newton Methods for Solving Nonsmooth Equations

This paper investigates inexact Newton methods for solving systems of nonsmooth equations. We de ne two inexact Newton methods for locally Lipschitz functions and we prove local (linear and superlinear) convergence results under the assumptions of semismoothness and BD-regularity at the solution. We introduce a globally convergent inexact iteration function based method. We discuss implementati...

Newton - Secant method for solving operator equations ∗

where F is a Fréchet-differentiable operator defined on an open subset D of a Banach space X with values in a Banach space Y . Finding roots of Eq.(1) is a classical problem arising in many areas of applied mathematics and engineering. In this study we are concerned with the problem of approximating a locally unique solution α of Eq.(1). Some of the well known methods for this purpose are the f...

The Comparison Adomian Decomposition Method and Differential Quadrature Method for Solving Some Nonlinear Partial Diferential Equations

Nonlinear partial diferential equations are a class of partial diferential equations having many important uses in engineering and sciences. In this work we display a comparison between Adomian Decomposition Method (ADM) and Differential Quadrature Method (DQM) for solving some nonlinear partial diferential equations. We found the existence of exact solutions for those models. The numerical res...

A Survey of Some Nonsmooth Equations and Smoothing Newton Methods

In this article we review and summarize recent developments on nonsmooth equations and smoothing Newton methods. Several new suggestions are presented.

Solving nonlinear integral equations in the Urysohn form by Newton-Kantorovich-quadrature method