Derivation and investigation of fifth order quadrature formulas for biharmonic boundary integral operators Original Research Article

Integral operators can conveniently be replaced by matrices through a quadrature followed by a collocation. For two operators related to biharmonic boundary integral equations we derive quadrature formulas with convergence order five. The fifth order convergence is obtained by an expedient change of the diagonal elements of the matrix; without this change the convergence order is only three. The method is investigated experimentally in case of a circular boundary curve by comparing the eigenvalues of the matrix with some of the eigenvalues of the integral operator. It turns out that this convergence is also of order five. This investigation has been carried out by an extensive use of the computer algebra system Maple V.