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A nonlocal problem for singular linear systems of ordinary differential equations

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Abstract

A system of linear ordinary differential equations is examined on an infinite half-interval. This system is supplemented by the boundedness condition for solutions and a nonlocal linear condition specified by the Stieltjes integral. A method for approximating the resulting problem by a problem posed on a finite interval is proposed, and the properties of the latter are investigated. A numerically stable method for solving this problem is examined. This method uses an auxiliary boundary value problem with separated boundary conditions.

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References

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Authors and Affiliations

  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    A. A. Abramov & V. I. Ul’yanova

  2. Institute of Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia

    L. F. Yukhno

Authors
  1. A. A. Abramov
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  2. V. I. Ul’yanova
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  3. L. F. Yukhno
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Correspondence to A. A. Abramov.

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Original Russian Text © A.A. Abramov, V.I. Ul’yanova, L.F. Yukhno, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 7, pp. 1228–1235.

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Abramov, A.A., Ul’yanova, V.I. & Yukhno, L.F. A nonlocal problem for singular linear systems of ordinary differential equations. Comput. Math. and Math. Phys. 51, 1146–1152 (2011). https://doi.org/10.1134/S0965542511070025

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  • DOI: https://doi.org/10.1134/S0965542511070025

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