Abstract: In this paper, we discuss some singulal integral operators, singular quadrature operators and discretization matrices associated with singular integral equations of the first kind, and obtain some useful Properties for them. Using these operators we give a unified framework for various collocation methods of numerical solutions of singular integral equations of the fine kind, which appears very simple.

Key words: Singalar interal operators, Singular quadrature operators, Discretization matrices, Extension operators, Collocation method