Solution for the singular integral equation with Hilbert Kernel based on wavelet

Many problems arising in mechanics and technology can be formulated as the first kind of singular integral equation. A Wavelet-Galerkin algorithm for solving the first kind of singular integral equation with Hilbert kernel was presented. In the algorithm the characteristic of periodic wavelet on L²([0,1]) and the Hilbert kernel were used to solve and make the stiff matrix lower dimension and become sparser through threshold. The computational amount was decreased and the memory space was saved. Because of the singularity of Hilbert kernel the Tikhonov regularization method was used to solve the stiff equation system. The convergence and the numerical result of approximate solution are discussed.