Fully-Discrete Collocation Methods for an Integral Equation of the First Kind

Abstract

Using a model boundary integral equation of the first kind, we study some very simple numerical integration schemes for implementing spline collocation methods. The logarithmic singularity in the kernel is handled by combining special correction terms with standard composite integration rules of Gauss or Lobatto type. We prove that the stability and asymptotic convergence properties of the collocation method are maintained despite the quadrature errors. Numerical experiments confirm the error analysis.