In the article, high-accuracy difference schemes for the Cauchy problem for a system of fourth-order equations are obtained. Based on the method of energy inequalities, the stability of the scheme is proved, a priori estimates of the solution to difference schemes are obtained, and their convergence and accuracy are proved. The results obtained for the system are applied to solve the first initial-boundary value problem for the equation of ion-acoustic waves in a "magnetized" plasma for the generalized potential of the electric field. The schemes constructed for this problem have second-order accuracy in spatial variables and fourth-order accuracy in time variables. In energy norms, convergence and accuracy estimates are obtained in classes of smooth solutions.
| Mualliflar | Aripov, M., Utebaev, D., Kdirbaev, S. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2026-03-25 |
| Jild | 70 |
| Son | 1 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2026-1-2 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2026-1-2 · Maqolaning asl sahifasi
Cauchy problem, fourth-order system of equations, ion-acoustic wave equation, difference schemes, approximation error, stability, convergence, accuracy
| APA | Aripov, M., Utebaev, D., & Kdirbaev, S. (2026). High-accuracy difference schemes for solving non-stationary fourth-order equations and their application to non-classical partial differential equations. O‘zbekiston matematika jurnali, 70(1). https://doi.org/10.29229/uzmj.2026-1-2 |
|---|---|
| GOST (OAK) | Aripov, M., Utebaev, D., Kdirbaev, S. High-accuracy difference schemes for solving non-stationary fourth-order equations and their application to non-classical partial differential equations // O‘zbekiston matematika jurnali. – 2026. – T. 70, № 1. – DOI: 10.29229/uzmj.2026-1-2. |
| MLA | Aripov, M., Utebaev, D., and Kdirbaev, S. “High-accuracy difference schemes for solving non-stationary fourth-order equations and their application to non-classical partial differential equations.” O‘zbekiston matematika jurnali, 70(1), 2026. https://doi.org/10.29229/uzmj.2026-1-2 |
| Chicago | Aripov, M., Utebaev, D., and Kdirbaev, S. “High-accuracy difference schemes for solving non-stationary fourth-order equations and their application to non-classical partial differential equations.” O‘zbekiston matematika jurnali, 70(1) (2026). https://doi.org/10.29229/uzmj.2026-1-2 |
| Harvard | Aripov, M., Utebaev, D., and Kdirbaev, S (2026) ‘High-accuracy difference schemes for solving non-stationary fourth-order equations and their application to non-classical partial differential equations’, O‘zbekiston matematika jurnali, 70(1). https://doi.org/10.29229/uzmj.2026-1-2 |
| BibTeX | @article{aripovm2026,
title = {High-accuracy difference schemes for solving non-stationary fourth-order equations and their application to non-classical partial differential equations},
author = {Aripov, M. and Utebaev, D. and Kdirbaev, S.},
journal = {O‘zbekiston matematika jurnali},
year = {2026},
volume = {70},
number = {1},
doi = {10.29229/uzmj.2026-1-2},
url = {https://doi.org/10.29229/uzmj.2026-1-2}
} |
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