1. Exponential Stability of the Numerical Solution of a Hyperbolic System with Nonlocal Characteristic Velocities.
- Author
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Aloev, Rakhmatillo Djuraevich, Berdyshev, Abdumauvlen Suleimanovich, Alimova, Vasila, and Bekenayeva, Kymbat Slamovna
- Subjects
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EXPONENTIAL stability , *BOUNDARY value problems , *NUMERICAL functions , *INITIAL value problems , *MEASUREMENT errors , *EXPONENTIAL dichotomy , *LYAPUNOV functions - Abstract
In this paper, we investigate the problem of the exponential stability of a stationary solution for a hyperbolic system with nonlocal characteristic velocities and measurement error. The formulation of the initial boundary value problem of boundary control for the specified hyperbolic system is given. A difference scheme is constructed for the numerical solution of the considered initial boundary value problem. The definition of the exponential stability of the numerical solution in ℓ 2 -norm with respect to a discrete perturbation of the equilibrium state of the initial boundary value difference problem is given. A discrete Lyapunov function for a numerical solution is constructed, and a theorem on the exponential stability of a stationary solution of the initial boundary value difference problem in ℓ 2 -norm with respect to a discrete perturbation is proved. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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