A Discrete Analog 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 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

References

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  4. Aloev R. D., Davlatov Sh. O., Eshkuvatov Z. K., Nik Long N. M. A. Uniqueness solution of the finite elements scheme for symmetric hyperbolic systems with variable coefficients// Malays. J. Math. Sci. - 2016. - 10 (S). - С. 49-60.
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