Non-Classical Quadrature Schemes for the Approximation of Cauchy Type Oscillatory and Singular Integrals in Complex Plane

Abstract

In this paper, non-classical numerical schemes are proposed for the approximation of Cauchy type oscillatory and strongly singular integrals in complex plane. The schemes are developed by incorporating classical quadrature rule meant for the Cauchy type complex singular integrals over a line segment in complex plane with a quasi exact quadrature method meant for the numerical integration of complex definite integrals with an oscillatory weight function. The error bounds are established and the schemes are numerically validated using a set of standard test integrals. Numerical results show that these schemes are efficient.