A wavelet-based solution of the Kuramoto-Sivashinsky equation

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.