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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 10, Pages 1721–1733
DOI: https://doi.org/10.31857/S0044466920090094 (Mi zvmmf11146) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Partial Differential Equations

On numerical solution of one class of integro-differential equations in a special case

N. S. Gabbasov

Naberezhnye Chelny Institute, Kazan Federal University, Naberezhnye Chelny, Republic of Tatarstan, 423810 Russia
Citations (8)
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DOI: https://doi.org/10.31857/S0044466920090094
Abstract: A complete theory of solvability of a linear integro-differential equation with a coefficient having power-law zeros is developed. For its approximate solution in the space of generalized functions, special generalized versions of the collocation method based on the use of standard polynomials and cubic splines of minimal defect are proposed and justified. Optimality in the order of accuracy of the method is established.
Key words: integro-differential equation, approximate solution, direct method, theoretical justification.
Received: 04.04.2020
Revised: 04.04.2020
Accepted: 09.07.2020
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 10, Pages 1666–1678
DOI: https://doi.org/10.1134/S0965542520090092
Bibliographic databases:
Document Type: Article
UDC: 519.642
Language: Russian
Citation: N. S. Gabbasov, “On numerical solution of one class of integro-differential equations in a special case”, Zh. Vychisl. Mat. Mat. Fiz., 60:10 (2020), 1721–1733; Comput. Math. Math. Phys., 60:10 (2020), 1666–1678
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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