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 |
| Nashr sanasi | 2026-03-25 |
| Jild | 70 |
| Son | 1 |
| Til | Ingliz |
| DOI | 10.29229/uzmj.2026-1-2 |
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
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