Computation of integrals over the unit circle with nearby poles Original Research Article

This paper deals with the computation of integrals over the unit circle T in the complex plane. Similar as for integrals on the real line, the presence of singularities near T affects adversely the estimation of the quadrature rules. In this paper we extend to integrals over the unit circle the method of subtracting out singularities. Application to the computation of integrals on the real line which occur frequently in the solution of boundary value problems for a circle, and comparison with other methods is made, showing the effectiveness of our method.