Exponential Stability of the Numerical Solution of a Hyperbolic System with Nonlocal Characteristic Velocities

Rakhmatillo Aloev, Abdumauvlen Suleimanovich Berdyshev, Vasila Alimova, Kymbat Bekenayeva

Axioms, 2024

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DOI 10.3390/axioms13050334
Data confidence 70 medium
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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 ℓ2-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 ℓ2-norm with respect to a discrete perturbation is proved.