A Discrete Analog of the Lyapunov Function for Hyperbolic Systems
- Authors: Aloev RD1, Khudayberganov MU1
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Affiliations:
- National University of Uzbekistan named after M. Ulugbek
- Issue: Vol 64, No 4 (2018): Contemporary Problems in Mathematics and Physics
- Pages: 591-602
- Section: New Results
- URL: https://journals.rudn.ru/CMFD/article/view/22276
- DOI: https://doi.org/10.22363/2413-3639-2018-64-4-591-602
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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 analog 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.
About the authors
R D Aloev
National University of Uzbekistan named after M. Ulugbek
Email: aloevr@mail.ru
M U Khudayberganov
National University of Uzbekistan named after M. Ulugbek
Email: mirzoali@mail.ru
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