Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Justification of a Galerkin method for a regularized Cauchy singular integro-differential equation


Author: A. I. Fedotov
Journal: Quart. Appl. Math. 67 (2009), 541-552
MSC (2000): Primary 45L05; Secondary 45E05, 65R20
DOI: https://doi.org/10.1090/S0033-569X-09-01138-3
Published electronically: May 12, 2009
MathSciNet review: 2547638
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For one class of the singular integro-differential equations with Cauchy kernel on an interval, a Galerkin method is justified. The convergence is proved and the error estimation is given.


References [Enhancements On Off] (What's this?)

  • 1. J. I. Frankel, A Galerkin solution to a regularized Cauchy singular integro-differential equation, Quart. Appl. Math. 2, 245-258 (1995). MR 1330651 (96b:45002)
  • 2. A. A. Badr, Integro-differential equation with Cauchy kernel, J. Comput. Appl. Math. 134, 191-199 (2001). MR 1852565 (2002e:65199)
  • 3. A. S. Peters, A note on the integral equation of the first kind with a Cauchy kernel, Comm. Pure Appl. Math. 21, 57-61 (1963). MR 0147859 (26:5372)
  • 4. F. D. Gakhov, Boundary Value Problems, Pergamon Press, Oxford, 1966. MR 0198152 (33:6311)
  • 5. M. A. Krasnosel'skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, V. Ya. Stetsenko, Approximate solution of operator equations, Noordhoff, Groningen, 1972. MR 0385655 (52:6515)
  • 6. B. G. Gabdulkhaev, Optimal approximations of solutions of linear problems, Kazan State University, Kazan, 1980 (in Russian). MR 630089 (83k:65047)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 45L05, 45E05, 65R20

Retrieve articles in all journals with MSC (2000): 45L05, 45E05, 65R20


Additional Information

A. I. Fedotov
Affiliation: Kazan State University, Research Institute of Mathematics and Mechanics, Kazan, 420008 Russia
Email: fedotov@mi.ru

DOI: https://doi.org/10.1090/S0033-569X-09-01138-3
Keywords: Singular integro-differential equations, Galerkin method
Received by editor(s): February 23, 2008
Published electronically: May 12, 2009
Dedicated: This paper is dedicated to Vladimir Baicher and Joellen Jarvi.
Article copyright: © Copyright 2009 Brown University
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society