Lyapunov stability of an upwind difference scheme for a quasilinear hyperbolic system

Authors

  • R. Aloev National University of Uzbekistan named after Mirzo Ulugbek Author
  • D. Nematova National University of Uzbekistan named after Mirzo Ulugbek Author
  • I. Abdullah Universiti Malaysia Terengganu Author
  • M. Mohd Universiti Malaysia Terengganu Author

DOI:

https://doi.org/10.29229/uzmj.2026-1-1

Keywords:

Exponential stability, hyperbolic system, mixed problem

Abstract

The paper considers a mixed problem for a quasilinear system of hyperbolic equations in Riemann invariants with dissipative nonlinear boundary conditions. To numerically solve the mixed problem, an initial-boundary difference problem based on an upwind difference scheme is proposed. A discrete Lyapunov function is constructed for the numerical solution of the initial-boundary difference problem for nonlinear problems. A theorem on the exponential stability of the stationary state of a quasilinear system is proven.

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Published

2026-03-25

Issue

Vol. 70 No. 1 (2026): Uzbek Mathematical Journal

Section

Others

How to Cite

Lyapunov stability of an upwind difference scheme for a quasilinear hyperbolic system. (2026). Uzbek Mathematical Journal, 70(1), 5-18. https://doi.org/10.29229/uzmj.2026-1-1