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dc.contributor.advisorUrintsev, Alexander
dc.contributor.authorRuiz-Valle, Gloria B.
dc.description.abstractThe 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.abstractEsta 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.subjectKuramoto-Sivashinsky equationen_US
dc.titleA wavelet-based solution of the Kuramoto-Sivashinsky equationen_US
dc.rights.licenseAll rights reserveden_US
dc.rights.holder(c) 2007 Gloria B. Ruiz-Valleen_US
dc.contributor.committeeRózga, Krzysztof
dc.contributor.committeeWalker, Uroyoán
dc.contributor.representativeCardona-Martínez, Nelson Mathematicsen_US
dc.contributor.collegeCollege of Arts and Sciences - Sciencesen_US
dc.contributor.departmentDepartment of Mathematicsen_US

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    Items included under this collection are theses, dissertations, and project reports submitted as a requirement for completing a graduate degree at UPR-Mayagüez.

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