Daubechies Wavelet Method for Second Kind Fredholm Integral Equations with Weakly Singular Kernel

Abstract

In this paper, the weakly singular Fredholm integral equations of the second kind are solved by the periodized Daubechies wavelets method. In order to obtain a good degree of accuracy of the numerical solutions, the Sidi-Israeli quadrature formulae are used to construct the approximation of the singular kernel functions. By applying the asymptotically compact theory, we prove the convergence of approximate solutions. In addition, the sidi transformation can be used to degrade the singularities when the kernel function is non-periodic. At last, numerical examples show the method is efficient and errors of the numerical solutions possess high accuracy order O (h 3+α), where h is the mesh size