Extrapolation Methods for Computing Hadamard Finite-Part Integral on Finite Intervals (Journal of Computational Mathematics, 2018)
In this paper, we present the composite rectangle rule for the computation of Hadamardfinite-part integrals in boundary element methods with the hypersingular kernel 1/(x−s)2 and we obtain the asymptotic expansion of error function of the middle rectangle rule.Based on the asymptotic expansion, two extrapolation algorithms are presented and theirconvergence rates are proved, which are the same as the Euler-Maclaurin expansions ofclassical middle rectangle rule approximations. At last, some numerical results are alsoillustrated to confirm the theoretical results and show the efficiency of the algorithms.
Keywords: Hadamard finite-part integral; Extrapolation method; Composite rectangle rule; Superconvergence; Error functional.