A quadrature method for constant-coefficient Cauchy singular integral equations on an interval

Abstract

AbstractWe consider a mesh grading quadrature method for real constant-coefficient Cauchy singular integral equations of index 0. The quadrature method is based on the trapezoidal rule. A complete stability and convergence analysis is given by the use of the noncompact perturbation analysis as in Jeon [10] and Elschner and Stephan [7]. The order of convergence can be arbitrarily high if the order of mesh grading is high enough. We also provide an efficient way of evaluating asymptotics of the solution at the end points. Experimentally, we observe that the method also works well for Cauchy singular integral equations with variable coefficients.