A Numerical Study on the Lyapunov Stability of Solutions to a Quasilinear Hyperbolic System
Rakhmatillo AloevComputational mathematics and information systems National University of Uzbekistan Tashkent city, Almazor district, University street, 4th house UZBEKISTANNematova DilfuzaComputational mathematics and information systems National University of Uzbekistan Tashkent city, Almazor district, University street, 4th house UZBEKISTAN
ABI
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.
Topics
Identifiers
Citations and references
Cited by 013 references
Metrics — AkademScholar · Coming soon