On a suitable quadrature for solving singular integral equation

Abstract

While solving Cauchy type singular integral equation via collocation procedure, the principal value integrals need to be approximated by suitable quadratures. This note highlights the superiority of the hyperbolic tangent quadrature for this purpose vis-a-vis conventional Gauss or Tchebyshev type quadratures. In particular, the ability to handle end point singularities of the integrand, arbitrary choice of collocation nodes combined with easy generation of nodes and efficiency are brought out by application to four test problems. IMT quadrature has also been adopted for this task but with less economy in computation.