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 |
| 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 | 53-66 |
| Til | Ingliz |
| DOI | 10.71310/pcam.3_67.2025.05 |
| Indeksga qo‘shilgan | 2026-08-27 |
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
| APA | Normurodov, Ch.B., Tilovov, M.A., Normurodov, D.Ch., Нормуродов, Ч.Б., Тиловов, М.А., & Нормуродов, Д.Ч. (2025). Numerical Modeling of the Amplitude Dynamics of the Stream Function for Plane Poiseuille Flow. Ҳисоблаш ва амалий математика муаммолари, (3), 53-66. https://doi.org/10.71310/pcam.3_67.2025.05 |
|---|---|
| GOST (OAK) | Normurodov, Ch.B. va b. Numerical Modeling of the Amplitude Dynamics of the Stream Function for Plane Poiseuille Flow // Ҳисоблаш ва амалий математика муаммолари. – 2025. – № 3. – P. 53-66. – DOI: 10.71310/pcam.3_67.2025.05. |
| MLA | Normurodov, Ch.B., Tilovov, M.A., Normurodov, D.Ch., Нормуродов, Ч.Б., Тиловов, М.А., and Нормуродов, Д.Ч. “Numerical Modeling of the Amplitude Dynamics of the Stream Function for Plane Poiseuille Flow.” Ҳисоблаш ва амалий математика муаммолари, (3), 53-66, 2025. https://doi.org/10.71310/pcam.3_67.2025.05 |
| Chicago | Normurodov, Ch.B., Tilovov, M.A., Normurodov, D.Ch., Нормуродов, Ч.Б., Тиловов, М.А., and Нормуродов, Д.Ч. “Numerical Modeling of the Amplitude Dynamics of the Stream Function for Plane Poiseuille Flow.” Ҳисоблаш ва амалий математика муаммолари, (3), 53-66 (2025). https://doi.org/10.71310/pcam.3_67.2025.05 |
| Harvard | Normurodov, Ch.B., Tilovov, M.A., Normurodov, D.Ch., Нормуродов, Ч.Б., Тиловов, М.А., and Нормуродов, Д.Ч (2025) ‘Numerical Modeling of the Amplitude Dynamics of the Stream Function for Plane Poiseuille Flow’, Ҳисоблаш ва амалий математика муаммолари, (3), 53-66. https://doi.org/10.71310/pcam.3_67.2025.05 |
| BibTeX | @article{normurodovchb2025,
title = {Numerical Modeling of the Amplitude Dynamics of the Stream Function for Plane Poiseuille Flow},
author = {Normurodov, Ch.B. and Tilovov, M.A. and Normurodov, D.Ch. and Нормуродов, Ч.Б. and Тиловов, М.А. and Нормуродов, Д.Ч.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2025},
number = {3},
pages = {53-66},
doi = {10.71310/pcam.3_67.2025.05},
url = {https://doi.org/10.71310/pcam.3_67.2025.05}
} |
Boshqa maqola uchun iqtibos tayyorlash
This article explores the significance of modifying SHAP (SHapley Additive exPlana tions) values to enhance model interpretability in machine learning. SHAP values provide a fair attribution of feature contributions…
Fractured porous media (FPM) in theoretical investigations is considered as a system of fractures and adjacent porous blocks (matrix). In such media, solute transport occurs mainly through the fracture system with mass…
This paper proposes a discrete model of the interaction between two airborne viruses, based on an operator acting in a four-dimensional simplex. The model describes the progression of an epidemic in a closed population…
The paper considers the radial problem of anomalous filtration of a homogeneous liquid in a plane-radial formulation. The filtration process was modeled by a differential equation with fractional derivatives with…
This article discusses the numerical modeling of the problem of nonlinear groundwater filtration taking into account evaporation and infiltration. Particular attention is paid to the influence of nonlinear effects on…
This paper first demonstrates that an algebraic-hyperbolic spline of eighth order minimizes the norm within a Hilbert space framework. Subsequently, employing Sobolev’s method, which involves constructing a discrete…
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…
There are algebraic and variational approaches of construction in the spline theory. In algebraic approach splines are considered as some smooth piecewise polynomial functions. In the variational approach splines are…
This study is devoted to the development of a system of equations for determining the coefficients of optimal interpolation formulas that integrate derivative information within a Hilbert space framework. Conventional…
This study explores the optimization of quadrature formulas for the approximate integration of periodic functions within a specific functional space. The research focuses on developing optimal quadrature formulas by…
Ҳисоблаш ва амалий математика муаммолари — barcha maqolalar · 2025-yil arxivi
To solve elliptic equations, iterative methods are mainly used, the number of iterations in which is often very large. For this reason, it is of interest to develop high-precision direct oriented methods for solving…
Many applied problems are described by the Dirichlet problem for the Poisson equa tions. This problem is used in the following practical situations: membrane or plate deflection, electric potential, gravitational and…
Many practical problems, such as a solar panel, a microplate inside an electronic device, a thin layer of metal exposed to a laser, or the bending of a reinforced concrete slab, are described by various boundary value…
The article studies the dynamics of derivatives up to the highest derivative of an ordinary differential equation of the fourth order with a small parameter at the highest derivative. The solution of the differential…
The article presents a numerical modeling approach for solving a non-homogeneous singularly perturbed fourth-order equation using by a discrete variant of the pre integration method. In the proposed method, the basis…
This paper presents a highly accurate and efficient spectral-grid method for the numerical solution of a boundary value problem for a fourth-order ordinary differential equation with a small parameter at the highest…