This study addresses a mixed problem for a quasilinear system of hyperbolic equations expressed in Riemann invariants, incorporating dissipative nonlinear boundary conditions. A numerical approach is developed through an initial-boundary difference problem utilizing an upwind difference scheme. The stability of nonlinear difference schemes is investigated, with a focus on establishing a sufficient stability criterion based on Lyapunov vector functions. The proposed criterion extends prior theoretical work, where a discrete Lyapunov function was formulated to demonstrate the exponential stability of the steady state for the quasilinear system. Numerical computations for a model problem validate these theoretical findings. The research highlights the potential of adapting the direct Lyapunov method to analyze the stability of nonlinear hyperbolic systems by constructing a positive definite function that exhibits monotonic decay along system solutions.
| Mualliflar | Aloev, R.D., Berdishev, A.S., Nematova, D.E., Алоев, Р.Д., Бердышев, А.С., Нематова, Д.Э. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashriyot | Тошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази |
| ISSN | 2181-8460, 2181-046X |
| Nashr sanasi | 2025-07-27 |
| Son | 3 |
| Betlar | 83-96 |
| Til | Ingliz |
| DOI | 10.71310/pcam.3_67.2025.07 |
| Indeksga qo‘shilgan | 2026-08-27 |
DOI: 10.71310/pcam.3_67.2025.07 · Maqolaning asl sahifasi
exponential stability, hyperbolic system, mixed problem, difference scheme, Lyapunov function, экспоненциальная устойчивость, гиперболическая система, смешанная задача, разностная схема, функция Ляпунова
| APA | Aloev, R.D., Berdishev, A.S., Nematova, D.E., Алоев, Р.Д., Бердышев, А.С., & Нематова, Д.Э. (2025). Numerical Study of Lyapunov Stability of an Upwind Difference Scheme for a Quasilinear Hyperbolic System. Ҳисоблаш ва амалий математика муаммолари, (3), 83-96. https://doi.org/10.71310/pcam.3_67.2025.07 |
|---|---|
| GOST (OAK) | Aloev, R.D. va b. Numerical Study of Lyapunov Stability of an Upwind Difference Scheme for a Quasilinear Hyperbolic System // Ҳисоблаш ва амалий математика муаммолари. – 2025. – № 3. – P. 83-96. – DOI: 10.71310/pcam.3_67.2025.07. |
| MLA | Aloev, R.D., Berdishev, A.S., Nematova, D.E., Алоев, Р.Д., Бердышев, А.С., and Нематова, Д.Э. “Numerical Study of Lyapunov Stability of an Upwind Difference Scheme for a Quasilinear Hyperbolic System.” Ҳисоблаш ва амалий математика муаммолари, (3), 83-96, 2025. https://doi.org/10.71310/pcam.3_67.2025.07 |
| Chicago | Aloev, R.D., Berdishev, A.S., Nematova, D.E., Алоев, Р.Д., Бердышев, А.С., and Нематова, Д.Э. “Numerical Study of Lyapunov Stability of an Upwind Difference Scheme for a Quasilinear Hyperbolic System.” Ҳисоблаш ва амалий математика муаммолари, (3), 83-96 (2025). https://doi.org/10.71310/pcam.3_67.2025.07 |
| Harvard | Aloev, R.D., Berdishev, A.S., Nematova, D.E., Алоев, Р.Д., Бердышев, А.С., and Нематова, Д.Э (2025) ‘Numerical Study of Lyapunov Stability of an Upwind Difference Scheme for a Quasilinear Hyperbolic System’, Ҳисоблаш ва амалий математика муаммолари, (3), 83-96. https://doi.org/10.71310/pcam.3_67.2025.07 |
| BibTeX | @article{aloevrd2025,
title = {Numerical Study of Lyapunov Stability of an Upwind Difference Scheme for a Quasilinear Hyperbolic System},
author = {Aloev, R.D. and Berdishev, A.S. and Nematova, D.E. and Алоев, Р.Д. and Бердышев, А.С. and Нематова, Д.Э.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2025},
number = {3},
pages = {83-96},
doi = {10.71310/pcam.3_67.2025.07},
url = {https://doi.org/10.71310/pcam.3_67.2025.07}
} |
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