Computational Method for A Certain Class of Singular Integral Equations Based on Wavelet

In this paper, Wavelet-Galerkin algorithm for solving the first kind of singular integral equations is presented. There are a lot of advantages to solve integral equations with Wavelet-Galerkin algorithm, such as the numerical sparsity of stiff matrix, the diagonal precondition procedure etc. A great deal of difficulties arises if we only use Wavelet-Galerkin algorithm to solve singular integral equations. This paper studies the solution to the first kind of singular integral equations based on wavelet. For the certain class of singular integral equations, this paper proposes Tikhonov regularization method to solve them. And at last the convergenceand numerical result of approximate solutions are discussed.