Solving singular integral equations using Gaussian quadrature and overdetermined systems

✍ Scribed by Erica Jen; Erica Jen; R.P. Srivastav

• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 468 KB
• Volume: 9
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(83)90120-7

✦ Synopsis

For singular integral equations of the Cauchy type on an open interval, a bounded solution exists only if an additional

condition is satisfied. In direct methods of solution when the integrals are replaced by quadratures, it is not obvious that the resulting discrete system of equations will be consistent. It is shown that for Gauss-Chebyshev quadrature, the overdetermined system of equations is consistent if and only if the discrete analog of the compatibility condition is satisfied. The behavior of solutions to inconsistent systems is examined.