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Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.]:
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Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2016, Issue 3, Pages 19–33 (Mi vtpmk18)  

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

Mathematical Modelling, Numerical Methods and Software Systems

Inverse problem for an ordinary integro-differential equation with degenerate kernel and nonlocal integral conditions

T. K. Yuldashev

Reshetnev Siberian State Aerospace University

Abstract: This article considers the questions of one value solvability of the nonlocal inverse problem for restore the resource and boundary regimes for a nonlinear Fredholm second-order ordinary integro-differential equation with degenerate kernel. By denoting the integro-differential equation is reduced to a system of algebraic equations with nonlinear right-hand side. This system is solved by the aid of modified Kramer method. By the aid of the given additional conditions is obtained the system of two equations with respect to first and second unknown quantity. Is derived also the formula for calculation the third unknown quantity. It is proved the one value solvability of this system by the method of successive approximations. Is derived also the formula for calculation the third unknown quantity. It is studied the stability of solution of the integro-differential equation with respect to restore quantities.

Keywords: nonlocal inverse problem, integro-differential equation, degenerate kernel, system of algebraic equations, one valued solvability.

DOI: https://doi.org/10.26456/vtpmk18

Full text: PDF file (316 kB)
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Document Type: Article
UDC: 517.9
Received: 10.09.2016
Revised: 30.09.2016

Citation: T. K. Yuldashev, “Inverse problem for an ordinary integro-differential equation with degenerate kernel and nonlocal integral conditions”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2016, no. 3, 19–33

Citation in format AMSBIB
\Bibitem{Yul16}
\by T.~K.~Yuldashev
\paper Inverse problem for an ordinary integro-differential equation with degenerate kernel and nonlocal integral conditions
\jour Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.]
\yr 2016
\issue 3
\pages 19--33
\mathnet{http://mi.mathnet.ru/vtpmk18}
\crossref{https://doi.org/10.26456/vtpmk18}
\elib{http://elibrary.ru/item.asp?id=27310773}


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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. T. K. Yuldashev, “Obobschennaya razreshimost smeshannoi zadachi dlya nelineinogo integro-differentsialnogo uravneniya vysokogo poryadka s vyrozhdennym yadrom”, Izv. IMI UdGU, 50 (2017), 121–132  mathnet  crossref  elib
    2. T. K. Yuldashev, “Ob odnoi nelokalnoi obratnoi zadache dlya nelineinogo integro-differentsialnogo uravneniya Benney-Luke s vyrozhdennym yadrom”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2018, no. 3, 19–41  mathnet  crossref  elib
  • Vestnik TVGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics]
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