Application of the discrete Fourier transform to solving the Cauchy integral equation

✍ Scribed by V.V. Kolybasova; P.A. Krutitskii; K.V. Prozorov; G. Vainikko

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 278 KB
• Volume: 235
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2010.08.017

✦ Synopsis

The uniquely solvable system of the Cauchy integral equation of the first kind and index 1 and an additional integral condition is treated. Such a system arises, for example, when solving the skew derivative problem for the Laplace equation outside an open arc in a plane. This problem models the electric current from a thin electrode in a semiconductor film placed in a magnetic field. A fast and accurate numerical method based on the discrete Fourier transform is proposed. Some computational tests are given. It is shown that the convergence is close to exponential.