M. A. Salanova

Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method

This study obtains two semilocal convergence results for the well-known Chebyshev method, which is a third-order iterative process. The hypotheses required are modifications to the normal Kantorovich ones. The results obtained are applied to the reduction of nonlinear integral equations of the Fredholm type and first kind.

ACCESSIBILITY OF SOLUTIONS BY NEWTON'S METHOD

We give new conditions for the convergence of Newtons method in Banach spaces, in terms of the degree of logarithmic convexity. These conditions guarantee the convergence of Newton sequence in cases where the hypothesis of Kantorovich theorem are not verified, as we show in some examples.

A discretization scheme for some conservative problems

We approximate a locally unique solution of an equation in Banach spaces using a Newton-like method of R-order three. Then we apply this method to obtain an existence-uniqueness result for a basic conservative problem given by a nonlinear boundary-value problem. Next, by means of a discretization method, we approximate the solution of the conservative problem.

Resolution of quadratic equations in banach spaces

A new convergence theorem is established for the super-Halley method. This method has, in general, order three, but when it is applied to quadratic equations, its order is four.

The application of an inverse-free Jarratt-type approximation to nonlinear integral equations of Hammerstein-type

Abstract We consider an inverse-free Jarratt-type approximation, whose order of convergence is four, for solving nonlinear equations. The convergence of this method is analysed under two different types of conditions. We use a new technique based on constructing a system of real sequences. Finally, this method is applied to the study of Hammersteins integral equations.

Solving nonlinear integral equations arising in radiative transfer

The super-Halley method is, in general, an iterative process with order of convergence three. In this paper we study this method in Banach spaces and we prove that the method converges with order four when it is applied to quadratic equations. Consequently, for this type of equations, the application of the super-Halley iteration could be of practical interest, aswe show in some examples: integral equations arising in radiative transfer.

A Newton-like Method for Solving Some Boundary Value Problems

ABSTRACT We use a Newton-like method for solving a nonlinear operator equation in a Banach space. A semilocal convergence result is provided in which the basic assumption is that the Frechet-derivative of the nonlinear operator is Hölder continuous on some open ball centered at the initial guess. We apply this study to solve a boundary value problem.

Solving a boundary value problem by a newton-like method

We present a semilocal convergence study where a Newton-like method is used to solve a boundary value problem of class M ; as an application of the previous study by means a scheme of discretization we approximate the solution of a particular problem.

A family of Chebyshev type methods in Banach Spaces

A family of third order iterative processes, that includes Chebyshev method, is studied in Banach Spaces. Results on convergence and uniqueness of solution are given, as well as error estimates.

Remark on the convergence of the midpoint method under mild differentiability conditions

Abstract We establish a convergence theorem for the Midpoint method using a new system of recurrence relations. The purpose of this note is to relax its convergence conditions. We also given an example where our convergence theorem can be applied but other ones cannot.