Adapted Newton-Kantorovich Methods for Nonlinear Integral Equations

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

SPLINE COLLOCATION FOR NONLINEAR FREDHOLM INTEGRAL EQUATIONS

The collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the integrand. Convergence analysis has been investigated and proved that the quadrature rule is third order convergent. The presented...

An Intermediate Newton Iterative Scheme and Generalized Zabrejko-nguen and Kantorovich Existence Theorems for Nonlinear Equations

We revisit a one-step intermediate Newton iterative scheme that was used by Uko and Velásquez in [17] for the constructive solution of nonlinear equations of the type f(u) + g(u) = 0 . By utilizing weaker hypotheses of the Zabrejko-Nguen kind and a modified majorizing sequence we perform a semilocal convergence analysis which yields finer error bounds and more precise information on the locatio...

On q-Newton-Kantorovich method for solving systems of equations

Starting from q-Taylor formula for the functions of several variables and mean value theorems in q-calculus which we prove by ourselves, we develop a new methods for solving the systems of equations. We will prove its convergence and we will give an estimation of the error. 2004 Elsevier Inc. All rights reserved.

Kantorovich-type convergence criterion for inexact Newton methods

Article history: Received 2 September 2008 Received in revised form 23 October 2008 Accepted 4 November 2008 Available online 13 November 2008 MSC: 65H10 65J15 47H30