Solving second kind integral equations by Galerkin methods with continuous orthogonal wavelets

In this paper, We use the continuous wavelets on the interval constructed by Cohen et al. (Appl. Comput. Harm. Anal. 1 (1993) 54–81) to solve the second kind integral equations. To this end, we give the decomposition and reconstruction algorithm for these wavelets, and construct the quadrature formulae for the calculation of inner products of any functions and the scaling functions, which are required in the wavelet-Galerkin methods for integral equations. In this method, the integral kernels are represented in these wavelet bases as sparse matrices, to high precision. Thus, we present an efficient algorithm for numerical solution of second kind integral equations.