EXISTENCE OF SOLUTIONS FOR A FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATION WITH UNBOUNDED DELAY

In this article, we study the existence of mild solutions for fractional neutral integro-differential equations with infinite delay.

3-D geometry reconstruction using a color image stereo pair and partial differential equations

[EN] In this work, we present a new model for a dense disparity estimation and the 3-D geometry reconstruction using a color image stereo pair. First, we present a brief introduction to the 3-D Geometry of a camera system. Next, we propose a new model for the disparity estimation based on an energy functional. We look for the local minima of the energy using the associate Euler-Langrage partial differential equations. This model is a generalization to color image of the model developed in, with some changes in the strategy to avoid the irrelevant local minima. We present some numerical experiences of 3-D reconstruction, using this method some real stereo pairs.

Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

Continued Fraction Solutions to Hermite's, Legendre's and Laguerre's Differential Equation

The continued fraction method for solving differential equations is illustrated using three famous differential equations used in quantum chemistry.

Nonlinear analysis of a simple model of temperature evolution in a satellite

We analyze a simple model of the heat transfer to and from a small satellite orbiting round a solar system planet. Our approach considers the satellite isothermal, with external heat input from the environment and from internal energy dissipation, and output to the environment as black-body radiation. The resulting nonlinear ordinary differential equation for the satellite’s temperature is analyzed by qualitative, perturbation and numerical methods, which prove that the temperature approaches a periodic pattern (attracting limit cycle). This approach can occur in two ways, according to the values of the parameters: (i) a slow decay towards the limit cycle over a time longer than the period, or (ii) a fast decay towards the limit cycle over a time shorter than the period. In the first case, an exactly soluble average equation is valid. We discuss the consequences of our model for the thermal stability of satellites.

Partial differential equations.

Mode of access: Internet.

Existence theorems in partial differential equations.

"Only the material on elliptic equations will appear in these notes."

Partial differential equations,

Mimeographed.

Plane waves and spherical means applied to partial differential equations.

Bibliography: p. 165-170.

A multirate ordinary differential equation integrator /

Originally presented as the author's thesis, University of Illinois at Urbana-Champaign.

An implicit method for the solution of elliptic partial differential equations.

Supported in part by National Science Foundation under Grant No. U.S. NSF-GJ-328.

Singular solutions at boundary intersections in two dimensional quasi-linear homogeneous partial differential equations /

Includes bibliographical references (20).

Automatic solutions of partial differential equations.

Vita.

Notes on partial differential equations.

Cover title.