Preliminary Study of Wavelet Method for Solving Ordinary Differential Equations

Abstract

Wavelet method is the backbone of various wavelet residue methods. In this context, Wavelet Galerkin Method is becoming a powerful tool to solve various type of differential equations. In this method, discrete orthogonal wavelets (family of functions with compact support) are used as shape functions which are easier to compute. These discrete orthogonal wavelets form a basis on a bounded domain. The connecting coefficients obtained by using Daubechies wavelet are presented to calculate the coefficient matrix. Initially we have considered an example problem and the general solutions of the same has been discussed by using wavelet Galerkin method. Then Haar wavelet has been studied in detail. Finally using wavelet method various example problems have been investigated. The obtained results are found to be in good agreement.