Computation of the orders of singularity of sectionally analytic functions

摘要

In several practical problems of science and engineering the solutions are expressed with the help of a sectionally analytic function with an open arc of discontinuity. A simple method is proposed here, on the basis of numerical integration rules, for the computation of the orders of singularity of this function at the tips of its arc of discontinuity. The values of these orders are of practical importance. Just the values of the sectionally analytic function (and, if possible, of its first derivative as well) on a closed contour surrounding the arc of discontinuity are required. Complex contour integrals are used for this evaluation. Numerical results are also displayed, and they illustrate the validity and the rapid convergence of the proposed computational technique. Generalizations of the approach are easily possible.