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Differential Equations

, Volume 55, Issue 2, pp 279–282 | Cite as

Improved Estimates of the Effect of Perturbations on the Solutions of Linear Differential-Algebraic Equations

  • V. F. ChistyakovEmail author
Short Communications
  • 6 Downloads

Abstract

We consider linear inhomogeneous vector systems of higher-order ordinary differential equations in which the coefficient of the highest derivative of the unknown vector function is a matrix identically singular in the domain where the system is defined. We study how perturbations of the system by a Volterra operator, as well as perturbations of the initial data and the free term, affect the solutions. The corresponding estimates are obtained, which are then used to justify the application of the least squares method to the numerical solution of the corresponding initial value problems.

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References

  1. 1.
    Chistyakov, V.F. and Chistyakova, E.V., Linear differential-algebraic equations perturbed by Volterra integral operators, Differ. Equations, 2017, vol. 53, no. 10, pp. 1274–1287.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Krasnov, M.L., Integral’nye uravneniya: vvedenie v teoriyu (Integral Equations: Introduction to the Theory), Moscow: Nauka, 1975.Google Scholar
  3. 3.
    Chistyakov, V.F. and Chistyakova, E.V., Application of the least squares method to solving linear differential-algebraic equations, Numer. Anal. Appl., 2013, vol. 6, no. 1, pp. 77–90.CrossRefzbMATHGoogle Scholar
  4. 4.
    Berezin, I.S. and Zhidkov, N.P., Metody vychislenii (Computation Methods), Moscow: Gos. Izd. Fiz. Mat. Lit., 1966, Vol. 1.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Matrosov Institute for System Dynamics and Control TheorySiberian Branch of the Russian Academy of SciencesIrkutskRussia

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