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
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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
- Jay I. Frankel, A Galerkin solution to a regularized Cauchy singular integro-differential equation, Quart. Appl. Math. 53 (1995), no. 2, 245–258. MR 1330651, DOI https://doi.org/10.1090/qam/1330651
- A. A. Badr, Integro-differential equation with Cauchy kernel, J. Comput. Appl. Math. 134 (2001), no. 1-2, 191–199. MR 1852565, DOI https://doi.org/10.1016/S0377-0427%2800%2900536-7
- A. S. Peters, A note on the integral equation of the first kind with a Cauchy kernel, Comm. Pure Appl. Math. 16 (1963), 57–61. MR 147859, DOI https://doi.org/10.1002/cpa.3160160108
- F. D. Gakhov, Boundary value problems, Pergamon Press, Oxford-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1966. Translation edited by I. N. Sneddon. MR 0198152
- M. A. Krasnosel′skiĭ, G. M. Vaĭnikko, P. P. Zabreĭko, Ya. B. Rutitskii, and V. Ya. Stetsenko, Approximate solution of operator equations, Wolters-Noordhoff Publishing, Groningen, 1972. Translated from the Russian by D. Louvish. MR 0385655
- B. G. Gabdulkhaev, Optimal′nye approksimatsii resheniĭ lineĭ nykh zadach, Kazan. Gos. Univ., Kazan′, 1980 (Russian). MR 630089
References
- 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)
- A. A. Badr, Integro-differential equation with Cauchy kernel, J. Comput. Appl. Math. 134, 191–199 (2001). MR 1852565 (2002e:65199)
- 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)
- F. D. Gakhov, Boundary Value Problems, Pergamon Press, Oxford, 1966. MR 0198152 (33:6311)
- 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)
- 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
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.
