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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 5, Pages 805–812 (Mi zvmmf467)  

This article is cited in 5 scientific papers (total in 5 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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:5, 768–775

Bibliographic databases:

UDC: 519.624.2
Received: 17.11.2005

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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\by N.~N.~Nefedov, A.~G.~Nikitin, T.~A.~Urazgil'dina
\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{http://www.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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746056017}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. N. Nefedov, A. G. Nikitin, “The Cauchy problem for a singularly perturbed integro-differential Fredholm equation”, Comput. Math. Math. Phys., 47:4 (2007), 629–637  mathnet  crossref  mathscinet  zmath
    2. N. N. Nefedov, A. G. Nikitin, “The initial boundary value problem for a nonlocal singularly perturbed reaction–diffusion equation”, Comput. Math. Math. Phys., 52:6 (2012), 926–931  mathnet  crossref  mathscinet  adsnasa  isi  elib  elib
    3. A. A. Archibasov, A. Korobeinikov, V. A. Sobolev, “Asymptotic expansions of solutions in a singularly perturbed model of virus evolution”, Comput. Math. Math. Phys., 55:2 (2015), 240–250  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. O. P. Filatov, “Globalnaya teorema suschestvovaniya i edinstvennosti resheniya pervoi kraevoi zadachi dlya nelineinogo integrodifferentsialnogo uravneniya parabolicheskogo tipa”, Vestn. SamGU. Estestvennonauchn. ser., 2015, no. 3(125), 64–72  mathnet  elib
    5. A. A. Bobodzhanov, V. F. Safonov, “A generalization of the regularization method to the singularly perturbed integro-differential equations with partial derivatives”, Russian Math. (Iz. VUZ), 62:3 (2018), 6–17  mathnet  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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