## Publication: A wavelet-based solution of the Kuramoto-Sivashinsky equation

 dc.contributor.advisor Urintsev, Alexander dc.contributor.author Ruiz-Valle, Gloria B. dc.contributor.college 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 dc.date.accessioned 2019-04-15T15:50:42Z dc.date.available 2019-04-15T15:50:42Z dc.date.issued 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.identifier.uri https://hdl.handle.net/20.500.11801/1983 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 thesis.degree.discipline Applied Mathematics en_US thesis.degree.level M.S. en_US
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