A Discrete Analog of the Lyapunov Function for Hyperbolic Systems

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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


  1. Блохин А. М., Алаев Р. Д. Интегралы энергии и их приложения к исследованию устойчивости разностных схем. - Новосибирск: Изд-во Новосибирского гос. ун-та, 1993.
  2. Годунов С. К. Уравнения математической физики. - М.: Наука, 1979.
  3. Aloev R. D., Blokhin A. M., Hudayberganov M. U. One class of stable difference schemes for hyperbolic system// Am. J. Numer. Anal. - 2014. - 2, № 3. - С. 85-89.
  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.
  5. Aloev R. D., Eshkuvatov Z. K., Davlatov Sh. O., Nik Long N. M. A. Sufficient condition of stability of finite element method for symmetric t-hyperbolic systems with constant coefficients// Comput. Math. Appl. - 2014. - 68, № 10. - С. 1194-1204.
  6. Bastin G., Coron J.-M. Stability and boundary stabilization of 1-D hyperbolic systems. - Basel: Birkha¨user, 2016.

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