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Stability of Solutions of Second-Order Differential-Operator Equations and of Their Difference Approximations

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Abstract

For the solutions of a nonlinear second-order differential-operator equation and the corresponding three-level operator-difference scheme, we establish sufficient boundedness conditions as well as sufficient conditions for the stability with respect to perturbations of the operators. These results are applied to studying the coefficient stability of a mixed problem for a hyperbolic equation with damping and a three-level difference scheme approximating this problem.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Belarus, Minsk, 220072, Belarus

    S. V. Lemeshevsky & P. P. Matus

  2. The John Paul Catholic University of Lublin, Lublin, 20-950, Poland

    P. P. Matus

Authors
  1. S. V. Lemeshevsky
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  2. P. P. Matus
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Correspondence to S. V. Lemeshevsky or P. P. Matus.

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Translated by V. Potapchouck

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Lemeshevsky, S.V., Matus, P.P. Stability of Solutions of Second-Order Differential-Operator Equations and of Their Difference Approximations. Diff Equat 56, 923–934 (2020). https://doi.org/10.1134/S0012266120070113

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  • DOI: https://doi.org/10.1134/S0012266120070113

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