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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 4, Pages 655–664 (Mi zvmmf304)  
This article is cited in 19 scientific papers (total in 19 papers)

The Cauchy problem for a singularly perturbed integro-differential Fredholm equation

N. N. Nefedov, A. G. Nikitin

Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
Full-text PDF (952 kB) Citations (19)
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Abstract: An initial problem is considered for an ordinary singularly perturbed integro-differential equation with a nonlinear integral Fredholm operator. The case when the reduced equation has a smooth solution is investigated, and the solution to the reduced equation with a corner point is analyzed. The asymptotics of the solution to the Cauchy problem is constructed by the method of boundary functions. The asymptotics is validated by the asymptotic method of differential inequalities developed for a new class of problems.
Key words: singularly perturbed integro-differential Fredholm equation, Cauchy problem, asymptotic technique, method of upper and lower solutions.
Received: 19.09.2006
English version:
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Issue 4, Pages 629–637
DOI: https://doi.org/10.1134/S0965542507040082
Bibliographic databases:
Document Type: Article
UDC: 519.642.2
Language: Russian
Citation: N. N. Nefedov, A. G. Nikitin, “The Cauchy problem for a singularly perturbed integro-differential Fredholm equation”, Zh. Vychisl. Mat. Mat. Fiz., 47:4 (2007), 655–664; Comput. Math. Math. Phys., 47:4 (2007), 629–637
Citation in format AMSBIB
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\paper The Cauchy problem for a~singularly perturbed integro-differential Fredholm equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\pages 655--664
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\transl
\jour Comput. Math. Math. Phys.
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\vol 47
\issue 4
\pages 629--637
\crossref{https://doi.org/10.1134/S0965542507040082}
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    • This publication is cited in the following 19 articles:
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