Convergence of numerical solution of the Fredholm integral equation of the first kind with degenerate kernel

Fredholm integral equation of the first kind is one of the ill posed problems since in the operator form of integral equation the integral operator does not have bounded inverse. In this article we consider integral equation of the first kind with degenerate kernel which has bounded inverse. We use collocation method by wavelet families for numerical solving of the equation. Then we prove the convergence for the numerical method. We use conjugate gradiant method for solving the system of linear equations after discretizing the integral equation. For showing efficiency of the method some examples are used.