A hyperbolic tangent quadrature rule for solving singular integral equations with Hadamard finite part integrals (Q1179394)

\textit{F. Stenger's} formula for numerical quadrature [J. Inst. Math. Appl. 12, 103-114 (1973; Zbl 0262.65011)]\ is suitable adapted for singular integrals as Hadamard finite part integrals. Convergence of that revised quadrature rule is studied in detail. A scheme for solving singular integral equations with Hadamard finite part integrals is proposed. The scheme is based on the revised hyperbolic tangent quadrature rule. The integral equation is reduced to a system of linear equations, by taking the same points as quadrature nodes and collocation points. The coefficient matrix of the system is shown to be nonsingular.