The numerical evaluation of a class of logarithmically singular integral transforms

摘要

We consider the numerical evaluation of several logarithmically singular integral transforms which occur in the numerical solution of various types of integral equations with logarithmically singular kernels. When the equations involve Cauchy singular kernels as well, the method is a substantial improvement in speed, accuracy, and ease of programming over the method introduced by Fromme, Golberg, and Werth [5]. Convergence of the rule is proved under suitable differentiability conditions on the “smooth” part of the kernel, and numerical results are presented substantiating this result.