Singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel

In a recent paper [3], Y. Cao and Y. Xu established the Galerkin method for weakly singular Fredholm integral equations that preserves the singularity of the solution. Their Galerkin method provides a numerical solution that is a linear combination of a certain class of basis functions which includes elements that reflect the singularity of the solution. The purpose of this paper is to extend the result of Cao and Xu and to establish singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. The iterated singularity preserving Galerkin method is also discussed.