Wavelet methods for boundary value problems

In this thesis modifications to the Wavelet Galerkin Method using Daubechies Wavelets will be presented. Such modifications are needed since the compact support of the scaling functions, used to approximate the solution, introduces significant errors near the boundaries of the domain of the problem. This thesis will point out the cause for these errors and remedies to minimize them. The variations of the Galerkin Method will be applied to several test cases, which include a differential equation with variable coefficients, and their results will presented. In addition, a presentation of Wavelet Theory and of the methods used to solve differential equations with constant coeffi-cients, that can be embedded in a periodic domain, will also be given.