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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 5, Pages 805–812 (Mi zvmmf467)  
This article is cited in 10 scientific papers (total in 10 papers)

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

N. N. Nefedov, A. G. Nikitin, T. A. Urazgil'dina

Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
Full-text PDF (954 kB) Citations (10)
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Abstract: The Cauchy problem for a singularly perturbed Volterra integro-differential equation is examined. Two cases are considered: (1) the reduced equation has an isolated solution, and (2) the reduced equation has intersecting solutions (the so-called case of exchange of stabilities). An asymptotic expansion of the solution to the Cauchy problem is constructed by the method of boundary functions. The results are justified by using the asymptotic method of differential inequalities, which is extended to a new class of problems.
Key words: singularly perturbed Volterra integro-differential equation, Cauchy problem, asymptotic method, differential inequalities.
Received: 17.11.2005
English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 5, Pages 768–775
DOI: https://doi.org/10.1134/S0965542506050046
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
Citation: N. N. Nefedov, A. G. Nikitin, T. A. Urazgil'dina, “The Cauchy problem for a singularly perturbed Volterra integro-differential equation”, Zh. Vychisl. Mat. Mat. Fiz., 46:5 (2006), 805–812; Comput. Math. Math. Phys., 46:5 (2006), 768–775
Citation in format AMSBIB
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\paper The Cauchy problem for a~singularly perturbed Volterra integro-differential equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 5
\pages 805--812
\mathnet{http://mi.mathnet.ru/zvmmf467}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2286277}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 5
\pages 768--775
\crossref{https://doi.org/10.1134/S0965542506050046}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746056017}
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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