Discrete quadrature method for singular integrals on closed smooth contours. – I. O. Isaac
In this paper, a discrete quadrature structure is worked out for the numerical solution of a singular integral of the form ∫Ω−=dtttttI00)()(ψ where t0 ∈ Ω, ψ(t) is smooth and belongs to the Holder’s class H(α) on Ω. Ω is a closed smooth contour, which may be a standard circle of radius r or a closed Lyapunov contour. Some numerical results are obtained for the case of a unit circle with center at the origin.
Keywords: Discrete quadrature method, Singular integral, Lyapunov contour.