A wavelet–galerkin method for the solution partial differential equation

Abstract

Wavelet function generates significant interest from both theoretical and applied research given in the last ten years. In the present project work, the Daubechies family of wavelets will be considered due to their useful properties. Since the contribution of compactly supported wavelet by Daubechies and multi resolution analysis based on Fast Fourier Transform (FWT) algorithm by Beylkin, wavelet based solution of ordinary and partial differential equations gained momentum in attractive way. Advantages of Wavelet-Galerkin Method over finite difference or element method have led to tremendous application in science and engineering.
In the present project work the Daubechies families of wavelets have been applied to solve differential equations. Solution obtained may the Daubechies-6 coefficients has been compared with exact solution. The good agreement of mathematical results , with the exact solution proves the accuracy and efficiency of Wavelet-Galerkin Method.