A wavelet-based solution of the Kuramoto-Sivashinsky equation

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Ruiz-Valle, Gloria B.
Embargoed Until
Urintsev, Alexander
College of Arts and Sciences - Sciences
Department of Mathematics
Degree Level
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.

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.
Kuramoto-Sivashinsky equation
Ruiz-Valle, G. B. (2007). A wavelet-based solution of the Kuramoto-Sivashinsky equation [Thesis]. Retrieved from