Lyapunov stability of the numerical solution of the Saint-Venant equation
Rakhmatillo AloevDepartment of Computational Mathematics and Information Systems, National University of Uzbekistan, Uzbekistan, Almazar 4, Tashkent, UzbekistanImran Ho AbdullahFaculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, MalaysiaAziza AkbarovaDepartment of Computational Mathematics and Information Systems, National University of Uzbekistan, Uzbekistan, Almazar 4, Tashkent, UzbekistanShuhrat JuraevDepartment of Computational Mathematics and Information Systems, National University of Uzbekistan, Uzbekistan, Almazar 4, Tashkent, Uzbekistan
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Аннотация
The work is devoted to the study of the stability of the finite difference method for the initial-boundary value problem for the system of Saint-Venant equations. Easily the verifiable practical stability conditions have been obtained. Energy estimates are established for an approximate solution of a discrete initial-boundary value problem. This energy estimate allows us to assert the stability of the finite difference method. The corresponding stability theorem is proved. The discrete Lyapunov function is constructed. An a priori estimate is obtained for the numerical solution of the boundary-value difference problem. This estimate allows us to speak about the exponential stability of the numerical solution.
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