O‘zbekiston matematika jurnali Volume 70 Issue 1 (2026)

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

Aloev, R., Nematova, D., Abdullah, I., Mohd, M.

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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.

Exponential stabilityhyperbolic systemmixed problem

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APA 7 
Aloev, R., Nematova, D., Abdullah, I. & Mohd, M. (2026). Lyapunov stability of an upwind difference scheme for a quasilinear hyperbolic system. O‘zbekiston matematika jurnali, 70(1).
GOST R 7.0.5 
Aloev, R., Nematova, D., Abdullah, I., Mohd, M. Lyapunov stability of an upwind difference scheme for a quasilinear hyperbolic system // O‘zbekiston matematika jurnali. 2026. Т. 70. № 1.
BibTeX 
@article{r.2026,
  author  = {Aloev, R. and Nematova, D. and Abdullah, I. and Mohd, M.},
  title   = {Lyapunov stability of an upwind difference scheme for a quasilinear hyperbolic system},
  journal = {O‘zbekiston matematika jurnali},
  year    = {2026},
  volume  = {70},
  number  = {1}
}
RIS 
TY  - JOUR
AU  - Aloev, R.
AU  - Nematova, D.
AU  - Abdullah, I.
AU  - Mohd, M.
TI  - Lyapunov stability of an upwind difference scheme for a quasilinear hyperbolic system
JO  - O‘zbekiston matematika jurnali
PY  - 2026
VL  - 70
IS  - 1
ER  -