On the wavelet-Galerkin method with Deslauriers-Dubuc interpolating scaling functions

Abstract

Compactly supported orthonormal wavelets are often used in numerical analysis. However, since these functions have not an explicit formula in the time domain, the difficulty of integrations often occurs. In this paper, we introduce the Galerkin method with Deslauriers-Dubuc interpolating scaling functions, and we use the biorthogonality of the wavelets to overcome the difficulties of integration. We present numerical results that show the efficiency and accuracy of this method.