Solving second kind Fredholm integral equations by periodic wavelet Galerkin method

In this paper, we use the periodized Daubechies wavelets based Galerkin method (PWGM) to solve linear, nonlinear and singular Fredholm integral equations of the second kind. A main advantage of the present PWGM over the existing wavelet Galerkin methods lies in that the wavelet expansion coefficients are exactly obtained without calculating the wavelet integrations. Therefore, the computational cost is low whereas the accuracy is high. After discretization, the linear and nonlinear integral equations is converted into a system of linear and nonlinear equations respectively, and for the linear case the matrix can be converted into a sparse and symmetrical one by Fast wavelet transform (FWT). Numerical experiments show that the PWGM has a good degree of accuracy.