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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 9, Pages 1579–1588 (Mi zvmmf4750)  

This article is cited in 2 scientific papers (total in 2 papers)

Properties of finite-difference schemes for singular integrodifferential equations of index 1

E. V. Chistyakova

Institute of Dynamic Systems and Control Theory, Siberian Branch, Russian Academy of Sciences, ul. Lermontova 134, Irkutsk, 664033, Russia

Abstract: Systems of integrodifferential equations with a singular matrix multiplying the highest derivative of the unknown vector function are considered. An existence theorem is formulated, and a numerical solution method is proposed. The solutions to singular systems of integrodifferential equations are unstable with respect to small perturbations in the initial data. The influence of initial perturbations on the behavior of numerical processes is analyzed. It is shown that the finite-difference schemes proposed for the systems under study are self-regularizing.

Key words: singular integrodifferential equations, difference solution method, influence of initial perturbations on the behavior of a numerical solution.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:9, 1507–1515

Bibliographic databases:

UDC: 519.62
Received: 11.01.2008
Revised: 16.03.2009

Citation: E. V. Chistyakova, “Properties of finite-difference schemes for singular integrodifferential equations of index 1”, Zh. Vychisl. Mat. Mat. Fiz., 49:9 (2009), 1579–1588; Comput. Math. Math. Phys., 49:9 (2009), 1507–1515

Citation in format AMSBIB
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\by E.~V.~Chistyakova
\paper Properties of finite-difference schemes for singular integrodifferential equations of index~1
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 9
\pages 1579--1588
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\pages 1507--1515
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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. M. V. Bulatov, E. V. Chistyakova, “On a family of singular integro-differential equations”, Comput. Math. Math. Phys., 51:9 (2011), 1558–1566  mathnet  crossref  mathscinet  isi
    2. N. D. Bang, V. F. Chistyakov, E. V. Chistyakova, “O nekotorykh svoistvakh vyrozhdennykh sistem lineinykh integro-differentsialnykh uravnenii. I”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 11 (2015), 13–27  mathnet
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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