Adapted linear approximation for singular integrals

Purpose: The purpose of this work is to present an approximation for singular integrals of Cauchy type kernel on a smooth-oriented contour. Methods: For the method, we use a small modification of the spline functions in order to eliminate the singularity. Noting that this approximation is due to the idea of Sanikidze's Approximate solution of singular integral equations in the case of closed contours of integrations. Results: This approximation represents a good approach for any singular integral given on the curve in the sense of Cauchy principal value. Conclusions: This approximation is destined to solve numerically the singular integral equations with Cauchy type kernel on a smooth-oriented contour.