Numerical solution of first kind Fredholm integral equations with wavelets-Galerkin method (WGM) and wavelets precondition

In this paper, we use orthogonal wavelets as basis in projection methods for obtaining numerical solution of the Fredholm integral equations of the first kind (FK1). If this basis has the MRA property, then we show that the projection methods, specially WGM, must be convergent. At the end, for showing efficiency of method we use some examples.