Numerical solution of Cauchy type singular integral equations with logarithmic weight, based on arbitrary collocation points

✍ Scribed by A. C. Chrysakis; G. Tsamasphyros

• Publisher: Springer
• Year: 1990
• Tongue: English
• Weight: 586 KB
• Volume: 7
• Category: Article
• ISSN: 0178-7675
• DOI: 10.1007/bf00370054

✦ Synopsis

Singular lntegral equations with a Cauchy type kernel and a logarithmic weight function can be solved numerically by integrating them by a Gauss-type quadrature rule and, further, by reducing the resulting equation to a linear system by applying this equation at an appropriate number of collocation points x~. Until now these x, have been chosen as roots of speclal functions. In this paper, an appropriate modification of the original method permits the arbitrary choice of x t without any loss in the accuracy. The performance of the method is examined by applying it to a numerical example and a plane crack problem.