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A Discrete Analogue of the Lyapunov Function for Hyperbolic Systems

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Abstract

We study the difference splitting scheme for the numerical calculation of stable solutions of a two-dimensional linear hyperbolic system with dissipative boundary conditions in the case of constant coefficients with lower terms. A discrete analogue of the Lyapunov function is constructed and an a priori estimate is obtained for it. The obtained a priori estimate allows us to assert the exponential stability of the numerical solution.

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References

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Authors and Affiliations

  1. National University of Uzbekistan named after M. Ulugbek, Tashkent, Uzbekistan

    R. D. Aloev & M. U. Hudayberganov

Authors
  1. R. D. Aloev
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  2. M. U. Hudayberganov
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Corresponding author

Correspondence to R. D. Aloev.

Additional information

Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 64, No. 4, Contemporary Problems of Mathematics and Physics, 2018.

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Aloev, R.D., Hudayberganov, M.U. A Discrete Analogue of the Lyapunov Function for Hyperbolic Systems. J Math Sci 264, 661–671 (2022). https://doi.org/10.1007/s10958-022-06028-y

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  • DOI: https://doi.org/10.1007/s10958-022-06028-y

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