QUADRATURES FOR BOUNDARY INTEGRAL EQUATIONS OF THE FIRST KIND WITH LOGARITHMIC KERNELS

YUESHENG XU AND YUNHE ZHAO

Abstract:

We consider boundary integral equations of the first kind with logarithmic kernels on smooth closed or open contours in . Instead of solving the first kind equations directly, we propose a fully discrete quadrature method for the equivalent second kind equations with kernels defined by Cauchy singular integrals simply using the trapezoidal integration rules. Convergence of the method is completely analyzed. It is proved that the order of convergence is , where n is the number of nodes in the quadrature formula and 2k+2 is the degree of smoothness of the righthand side function of the equation. Numerical examples are presented to confirm the theoretical estimate.