Article

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

R. AloevNational University of Uzbekistan named after Mirzo UlugbekD. NematovaNational University of Uzbekistan named after Mirzo UlugbekI. AbdullahUniversiti Malaysia TerengganuM. MohdUniversiti Malaysia Terengganu

Uzbek Mathematical Journaljournal2026

ABI

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.

Topics

Stability and Controllability of Differential Equations Differential Equations and Boundary Problems Soil, Finite Element Methods

Identifiers

DOI: 10.29229/uzmj.2026-1-1

Citations and references

Cited by 00 references

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