Taylor expansion method for integrals with algebraic-logarithmic singularities

In this paper, a method based on Taylor's polynomials is presented to approximate a singular integral with the integrand of the form f(t) k(t, c), where f(t) is a given smooth function and k(t, c) is a kernel possing algebraic-logarithmic singularity at the point c∈[a, b], (−1≤a, b, c≤1). The function f(t) is approximated by Taylor polynomials. Therefore, the integrand can be expressed in terms of algebraic-logarithmic functions. To get higher accuracy, the integration domain is divided into M subintervals and the methods are used on subintervals. The main advantage of the proposed method is its simplicity in use and its high accuracy. Numerical examples illustrated the pertinent features of the method.