Computational methods for integrals involving functions and Daubechies wavelets

When wavelets are used as basis functions in Galerkin approach to solve the integral equations, Integrals of the form integral(supp(theta j,k))f(x)theta(j,k)(x) dx occur. By a change of variable, these integrals can be translated into integrals involving only theta. In this paper, we find quadrature rule on the supp(theta) for the integrals of the form integral(supp(theta))f(x)theta dx, theta is an element of {phi,psi}. Wavelets in this article are those discovered by Daubechies [I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988) 909-996], where phi is the scaling function and psi is the wavelet function. (c) 2007 Elsevier Inc. All rights reserved.