Computational methods for integrals involving functions and Daubechies wavelets

摘要

When wavelets are used as basis functions in Galerkin approach to solve the integral equations, Integrals of the form ∫supp(θj,k)f(x)θj,k(x)dx occur. By a change of variable, these integrals can be translated into integrals involving only θ. In this paper, we find quadrature rule on the supp(θ) for the integrals of the form∫supp(θ)f(x)θ(x)dx,θ∈{ϕ,ψ}.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 ϕ is the scaling function and ψ is the wavelet function.