Examinando por Materia "Ecuaciones diferenciales - Análisis"
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Ítem Una aproximación a los polinomios casi-ortogonalesMonserrate Sepúlveda, Miguel Antonio; Sanjuán Cuéllar, Álvaro ArturoThe purpose of this work is to analyze the article "On quasi-orthogonal polynomials" written by David Dickinson. For this, in the first place some theoretical bases are established that serve as tools to be able to give a good development to the work. Following this the general theory of orthogonal polynomials is stated and it is shown that given a sequence of orthogonal polynomials a relationship of 3 terms is fulfilled, as well as a particular case in which orthogonal polynomials have real coefficients. Finally, a general definition of quasi-orthogonal polynomials is presented, two necessary and sufficient condition theorems that show the strong relationship that exists between orthogonal polynomials and quasi-orthogonal polynomials, a third necessary and sufficient condition theorem about quasi-orthogonal polynomials, and as an example that Sister Celine's polynomials are quasi-orthogonal.Ítem Perturbaciones singulares sobre una clase de ecuaciones diferencialesRamírez Parada, David Leonardo; Sanjuán Cuéllar, Álvaro ArturoIn this paper we deal with a particular equation of a class of partial differential equations. We focus on the continuity of the solution which is given by the method of characteristic curves. More specifically, the generalized Burgers equation. This is a differential equation well known for mathematical analysis and for its applications. It is commonly used in traffic flow and fluid motion models. In finite time there is a singularity also called blow-up that generates discontinuities even if the initial conditions are continuous. We describe the continuous solution given by the singularity. And we employ the singular perturbation technique to find a correction to the position at the discontinuity.