| Title:
|
On convergence of quadrature-differences method for linear singular integro-differential equations on the interval (English) |
| Author:
|
Fedotov, A. I. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
37 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
257-271 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Here we propose and justify the quadrature-differences method for the full linear singular integro-differential equations with Cauchy kernel on the interval $(-1,1)$. We consider equations of zero, positive and negative indices. It is shown, that the method converges to exact solution and the error estimate depends on the sharpness of derivative approximation and the smoothness of the coefficients and the right-hand side of the equation. (English) |
| Keyword:
|
singular integro-differential equations |
| Keyword:
|
quadrature-differences method |
| MSC:
|
45E05 |
| MSC:
|
45L05 |
| MSC:
|
65R20 |
| idZBL:
|
Zbl 1090.45003 |
| idMR:
|
MR1879448 |
| . |
| Date available:
|
2008-06-06T22:29:03Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107803 |
| . |
| Reference:
|
[1] Afendikova N. G., Lifanov I. K., Matveev A. F.: Approximate solution of singular integral equations.Differ. Uravn. 23 (1987), N8, 1392–1402 (in Russian). Zbl 0645.65092, MR 0909586 |
| Reference:
|
[2] Belotserkovski S. M., Lifanov I. K.: Numerical methods for singular integral equations.Moscow 1985 (in Russian). |
| Reference:
|
[3] Elliott D.: The approximate solution of singular integral equations.Solution Methods for Integral Equations, Theory and Applications, Math. Concepts Meth. Sci. Eng., New York-London 18 1979, 83–107. Zbl 0446.65062, MR 0564265 |
| Reference:
|
[4] Fedotov A. I.: On convergence of quadrature-differences method for linear singular integrodifferential equations.Zh. Vychisl. Mat. Mat. Fiz. 29 (1989), N9, 1301–1307 (in Russian). MR 1018581 |
| Reference:
|
[5] Fedotov A. I.: On convergence of quadrature-differences method for one class of singular integro-differential equations.Izv. Vyssh. Uchebn. Zaved. Mat. (1989), N8, 64–68 (in Russian). MR 1039732 |
| Reference:
|
[6] Fedotov A. I.: On convergence of quadrature-differences method for nonlinear singular integrodifferential equations.Zh. Vychisl. Mat. Mat. Fiz. 31 (1991), N5, 781–787 (in Russian). MR 1120019 |
| Reference:
|
[7] Fedotov A. I.: On convergence of quadrature-differences method for linear singular integrodifferential equations with discontinuous coefficients.Zh. Vychisl. Mat. Mat. Fiz. 31 (1991), N2, 261–271 (in Russian). MR 1099589 |
| Reference:
|
[8] Gakhov F. D.: Boundary Value Problems.Pergamon Press, Oxford, England 1966. Zbl 0141.08001, MR 0198152 |
| Reference:
|
[9] Hvedelidze B. V.: Linear discontinuous boundary problems of the theory of functions and some their applications.Proceedings of Tbilisi Mathematical Institute of Georgian Academy of Sciences 23 (1956), 3–158 (in Russian). MR 0107148 |
| Reference:
|
[10] Ivanov V. V.: The theory of approximate methods and their application to the numerical solution of singular integral equations.Noordhoff, Holland 1976. Zbl 0346.65065, MR 0405045 |
| Reference:
|
[11] Kantorovič L. V., Akilov G. P.: Functional analysis in normed spaces.Macmillan, New York 1964. MR 0213845 |
| Reference:
|
[12] Karpenko L. N.: Approximate solution of a singular integral equations by means of Jacobi polynomials.J. Appl. Math. Mech. 30 (1966), 668–675. MR 0231156 |
| Reference:
|
[13] Lifanov I. K.: The method of singular integral equations and a numerical experiment in mathematical physics, aerodynamics and the theory of elasticity and wave diffraction.Moscow 1995 (in Russian). Zbl 0904.73001, MR 1461016 |
| Reference:
|
[14] Matveev A. F.,: On the construction of approximate solutions of singular integral equations of the second kind.Doklady Akad. Nauk 307 (1989), N5, 1046–1050 (in Russian). MR 1020685 |
| Reference:
|
[15] Muskhelishvili N. I.: Singular integral equations.Noordhoff, Groningen, Holland 1953. Zbl 0051.33203, MR 0355494 |
| Reference:
|
[16] Natanson I. G.: Construction theory of functions.Moscow 1959 (in Russian). |
| Reference:
|
[17] Szegö G.: Orthogonal Polynomials.AMS Colloquim Publications, 23, 1967. MR 0310533 |
| Reference:
|
[18] Vainikko G. M.: The compact approximation of the operators and the approximate solution of the equations.Tartu University Press, Tartu 1970 (in Russian). MR 0273475 |
| . |
