A wavelet-based solution of the Kuramoto-Sivashinsky equation

dc.contributor.advisor Urintsev, Alexander Ruiz-Valle, Gloria B. College of Arts and Sciences - Sciences en_US
dc.contributor.committee Rózga, Krzysztof
dc.contributor.committee Walker, Uroyoán
dc.contributor.department Department of Mathematics en_US
dc.contributor.representative Cardona-Martínez, Nelson 2019-04-15T15:50:42Z 2019-04-15T15:50:42Z 2007
dc.description.abstract The scope of this thesis investigation is to obtain an approximate numerical solution to the nonlinear one-dimensional Kuramoto-Sivashinsky partial differential equation. The Gaussian wave has been successfully applied to convert this equation by means of a wavelet transform into a nonlinear integro-differential equation for the transformant. A Cauchy problem was formulated. The wavelet coefficients were expanded by means of basis functions based on the classical Laguerre and Hermite orthogonal polynomials, and then the Galerkin method was used to get a system of ordinary differential equations that was solved numerically with the Mathematica system. en_US
dc.description.abstract Esta tesis describe cómo obtener una solución numérica para la ecuación diferencial parcial no lineal de Kuramoto–Sivashinsky en una dimensión. La ondita (wavelet) “Gaussian wave” ha sido aplicada con éxito para convertir esta ecuación en una ecuación no lineal integro-diferencial para el transformante a través de una transformación de ondita. Se formuló un problema de Cauchy. Los coeficientes de ondita fueron expandidos a través de funciones bases fundamentadas en los polinomios ortogonales clásicos de Hermite y de Laguerre y entonces el método de Galerkin se usó para obtener un sistema de ecuaciones diferenciales ordinarias que fue resuelto numéricamente utilizando el sistema Mathematica. en_US
dc.description.graduationYear 2007 en_US
dc.language.iso English en_US
dc.rights.holder (c) 2007 Gloria B. Ruiz-Valle en_US
dc.rights.license All rights reserved en_US
dc.subject Kuramoto-Sivashinsky equation en_US
dc.title A wavelet-based solution of the Kuramoto-Sivashinsky equation en_US
dc.type Thesis en_US
dspace.entity.type Publication Applied Mathematics en_US M.S. en_US
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