Padé approximants for the numerical solution of singular integral equations

Abstract

A method for accelerating the convergence of the numerical solution of a singular integral equation, based on Pade  Approximants, is given in this paper. At ®rst the general form of the Pade  Table and of the``epsilon'' algorithm are presented. Taking into consideration the classical quadrature method, based on the GaussJacobi quadrature rule, an approximate formula is derived for the unknown density function of the Cauchy-type singular integral equation or of the equivalent Fredholm integral equation. In this formula applying the``epsilon'' algorithm to the solution for the stress intensity factors, the convergence is achieved after a few operations. The number of numerical operations required for the determination of stress intensity factors is considerable reduced, when compared to the number of operations required for a classical type of solution. Illustrative examples are given, indicating the ef®ciency of the method.

Boundary integral equation method to solve embedded planar crack problems under shear loading

“…The convergence for the stress intensity factor may also be improved using Padé Approximation [38]. The proposed method is limited to plane cracks with smoothcontour shape.…”