Pedro Medeiros - Academia.edu (original) (raw)

Papers by Pedro Medeiros

Communications on Pure and Applied Analysis, 2006

In this work we are concerned about a second order nonlinear ordinary differential equation. Our ... more In this work we are concerned about a second order nonlinear ordinary differential equation. Our main purpose is to describe one-parameter families of solutions of this equation which satisfy certain boundary conditions. These one-parameter families of solutions are obtained in the form of asymptotic or convergent series. The series expansions are then used to approximate the solutions of two boundary value problems. We are specially interested in the cases where these problems are degenerate with respect to the unknown function and/or to the independent variable. Lower and upper solutions for each of the considered boundary value problems are obtained and, in certain particular cases, a closed formula for the exact solution is derived. Numerical results are presented and discussed.

Applied Numerical Mathematics, 1999

In the present paper we are concerned with boundary-value problems (BVP) for the generalized Emde... more In the present paper we are concerned with boundary-value problems (BVP) for the generalized Emden-Fowler equations. Asymptotic expansions of the solution are obtained near the endpoints. We use a finite-difference scheme to approximate the solution and the convergence is accelerated by means of extrapolation methods. A variable substitution is introduced to diminish the effect of the singularity at the origin. Numerical results, obtained by different methods, are presented for two particular cases.

Journal of Computational and Applied Mathematics, 2007

We consider the qualitative behaviour of solutions to linear integral equations of the form

Journal of Computational and Applied Mathematics, 2010

This paper is concerned with the approximate solution of a linear non-autonomous functional diffe... more This paper is concerned with the approximate solution of a linear non-autonomous functional differential equation, with both advanced and delayed arguments. We search for a solution

Journal of Computational and Applied Mathematics, 2009

In this paper we are concerned about a singular boundary value problem for a quasilinear second-o... more In this paper we are concerned about a singular boundary value problem for a quasilinear second-order ordinary differential equation, involving the one-dimensional p-laplacian. Asymptotic expansions of the one-parameter families of solutions, satisfying the prescribed boundary conditions, are obtained in the neighborhood of the singular points and this enables us to compute numerical solutions using stable shooting methods.

This paper is concerned with the approximate solution of a functional differential equation of th... more This paper is concerned with the approximate solution of a functional differential equation of the form:

Journal of Computational and Applied Mathematics, 1999

We consider a second-order nonlinear ordinary differential equation of the formy″=1qxyq,0⩽x&l... more We consider a second-order nonlinear ordinary differential equation of the formy″=1qxyq,0⩽x<1where q<0, with the boundary conditionsy′(0)=y(1)=0.This problem arises in boundary layer equations for the flow of a power-law fluid over an impermeable, semi-infinite flat plane. We show that classical iterative schemes, such as the Picard and Newton methods, converge to the solution of this problem, in spite of the singularity of the solution, if we choose an adequate initial approximation. Moreover, we observe that these methods are more efficient than the methods used before and may be applied to a larger range of values of q. Numerical results for different values of q are given and compared with the results obtained by other authors.

Communications on Pure and Applied Analysis, 2004

This work is concerned with the construction and analysis of high order product integration metho... more This work is concerned with the construction and analysis of high order product integration methods for a class of Volterra integral equations with logarithmic singular kernel. Sufficient conditions for the methods to be convergent are derived and it is shown that optimal convergence orders are attained if the exact solution is sufficiently smooth. The case of non-smooth solutions is dealt with by making suitable transformations so that the new equation possesses smooth solutions. Two particular methods are considered and their convergence proved. A sample of numerical examples is included.

Journal of Computational and Applied Mathematics, 2002

In this work the numerical solution of a Volterra integral equation with a certain weakly singula... more In this work the numerical solution of a Volterra integral equation with a certain weakly singular kernel, depending on a real parameter , is considered. Although for certain values of this equation possesses an inÿnite set of solutions, we have been able to prove that Euler's method converges to a particular solution. It is also shown that the error allows an asymptotic expansion in fractional powers of the stepsize, so that general extrapolation algorithms, like the E-algorithm, can be applied to improve the numerical results. This is illustrated by means of some examples.

Frontiers of Mathematics in China, 2009