Richardson Extrapolation Applied to the Numerical Solution of Boundary Integral Equations for a Laplace's Equation Dirichlet Problem

Richardson extrapolation is applied to improve the accuracy of the numerical solution of boundary integral equations.The boundary integral equations arise from a direct boundary integral method for solving a Laplace's equation interior Dirichlet problem.Specifically, the Richardson extrapolation is used to improve the accuracy of collocation.Numerical justification is provided to support the expectation of improved accuracy.The order of the dominant collocation error term is numerically estimated and numerical results are obtained for a simple model problem.