WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
A Numerical Study on the Lyapunov Stability of Solutions to a Quasilinear Hyperbolic System
Authors: ,
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Abstract: This paper addresses the numerical study of the exponential stability of the initial-boundary value
problem for a quasilinear system of hyperbolic equations expressed in Riemann invariants, with dissipative
nonlinear boundary conditions. To numerically solve this initial-boundary value problem, we propose utilizing
a difference scheme based on an upwind method. The discrete Lyapunov function is presented as a tool for the
numerical solution of the initial-boundary value difference problem, and its effectiveness is supported through
various examples. Furthermore, the conditions outlined in the theorem concerning the exponential stability of the
stationary state of a quasilinear system are numerically analyzed.
Keywords:
Exponential stability, hyperbolic system, mixed problem, Lyapunov function, nonlinear difference
scheme, numerical solution, boundary conditions
Pages: 526-537
DOI: 10.37394/23206.2025.24.52