This paper investigates the dynamics of the complex amplitude of the stream function for plane Poiseuille flow using the spectral method. An approximate solution of the flow under consideration is sought as a finite series expansion in terms of Chebyshev polynomials of the first kind with unknown expansion coefficients. The eigenvalue spectrum of the Poiseuille flow is determined, and the most unstable eigenvalue (with the largest modulus) is selected. The components of the corresponding eigenvector, which represent the complex unknown coefficients of the desired series expansion, are also determined. Using these coefficients, the real and imaginary parts of the amplitude of the stream function for the perturbed flow are computed. The results of the computations are presented in both tabular and graphical form and demonstrate the high accuracy of the proposed approach.
| Mualliflar | Normurodov, Ch.B., Tilovov, M.A., Normurodov, D.Ch., Нормуродов, Ч.Б., Тиловов, М.А., Нормуродов, Д.Ч. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashr sanasi | 2025-07-27 |
| Son | 3 |
| Betlar | 53-66 |
| Til | Rus |
| DOI | 10.71310/pcam.3_67.2025.05 |
DOI: 10.71310/pcam.3_67.2025.05 · Maqolaning asl sahifasi
Poiseuille flow, stream function amplitude, spectral method, Chebyshev polynomials, high accuracy, течение Пуазейля, амплитуда функции тока, спектральный метод, полиномы Чебышева, высокая точность
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