Extrapolation methods for spline collocation solutions of pseudodifferential equations on curves

SummaryIn this article we consider extrapolation methods in approximating smooth linear functionals by means of collocation solutions of boundary integral equations. We are able to derive an asymptotic expansion of the error. In main applications this expansion covers arbitrary high powers of the discretization parameter if the boundary solution is smooth. The expansion gives rise to Richardson-type extrapolation schemes which require only simple postprocessing of calculated numbers. The results are applicable for example in calculating pointwise values in the space domain, when solving boundary value problems by means of integral equations. In such examples the extrapolation rapidly improves the original rate of the convergence. Numerical experiments conform our results.