Numerical solution of Fredholm integral equations of the first kind by using Legendre wavelets

An efficient method based on the Legendre wavelet approach is proposed for approximate the solution of Fredholm integral equations of the first kind. The continues Legendre wavelets constructed on [0, 1] are utilized as a basis in Galerkin method to reduce the solution of linear integral equations to a system of algebraic equations. For solving this system, we use the CG method. Furthermore, we suggest a convergence analysis and error estimation for this method. For showing efficiency of method some test problems, for which the exact solution is known, are considered.