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Justification of a Galerkin method for a regularized Cauchy singular integro-differential equation
Author(s):
A.
I.
Fedotov
Journal:
Quart. Appl. Math.
67
(2009),
541-552.
MSC (2000):
Primary 45L05;
Secondary 45E05, 65R20
Posted:
May 12, 2009
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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:
-
- 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)
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Additional Information:
A.
I.
Fedotov
Affiliation:
Kazan State University, Research Institute of Mathematics and Mechanics, Kazan, 420008 Russia
Email:
fedotov@mi.ru
PII:
S0033-569X-09-01138-3
Keywords:
Singular integro-differential equations,
Galerkin method
Received by editor(s):
February 23, 2008
Posted:
May 12, 2009
Dedicated:
This paper is dedicated to Vladimir Baicher and Joellen Jarvi.
Copyright of article:
Copyright
2009,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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