Open AccessA Discrete Analog of the Lyapunov Function for Hyperbolic Systems
Author(s) -
Rakhmatillo Aloev,
R. D. Alaev,
Mirzoali Khudayberganov,
М У Худайберганов
Publication year - 2018
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2018-64-4-591-602
Subject(s) - dissipative system , lyapunov function , mathematics , a priori and a posteriori , constant (computer programming) , boundary (topology) , function (biology) , mathematical analysis , exponential function , stability (learning theory) , computer science , physics , nonlinear system , philosophy , epistemology , quantum mechanics , evolutionary biology , machine learning , biology , programming language
We study the dierence 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 coecients 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.