Investigation of the Exponential Stability of the Numerical Solution of a Hyperbolic System with Negative Nonlocal Characteristic Velocities
DOI:
https://doi.org/10.71310/pcam.4_68.2025.05Keywords:
Hyperbolic equation, nonlocal characteristic velocity, stability, explicit difference schemeAbstract
In this work, the problem of stabilizing the equilibrium state for a hyperbolic equation with negative nonlocal characteristic velocity and measurement error is investigated. The formulation of the mixed control problem is presented. The weak solution, exponential stability of the equilibrium state of the mixed problem, and the definition of the Lyapunov function are given. The exponential stability of the equilibrium state of a mixed problem is given. The stability in the ????2 – norm is determined relative to the discrete perturbations of the equilibrium state of the initial-boundary difference problem. In a computational experiment, one hyperbolic equation with negative characteristic velocity was considered and its numerical solution was found using the constructed difference scheme. The graph of the norm ????2 of the numerical solution, demonstrating its stability, is shown.
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