This paper studies the dynamics of derivatives of various orders of the Falkner–Skan (FS) equation in the presence of a longitudinal pressure gradient. The FS equation is a nonlinear singularly perturbed third-order equation, and the behaviour of its solution and derivatives for various values of the form parameter ????, which is related to the pressure gradient, remains largely unexplored. The first derivative determines the velocity profile of the main flow in the boundary layer and is important for hydrodynamic stability analysis. The FS equation is reduced to a Cauchy problem for three nonlinear first-order ordinary differential equations, solved by the fourth-order Runge–Kutta method in vector form. Results are obtained for positive, zero, and negative pressure gradients. At ???? = 0 the profile coincides with the Blasius profile; for ???? < 0 the boundary layer thickens and may separate; for ???? > 0 its thickness decreases.
| Mualliflar | Тиловов, М.А., Tilovov, M.A. |
|---|---|
| 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 | 2026-07-02 |
| Son | 3 |
| Betlar | 139-152 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.71310/pcam.3_73.2026.10 |
| Indeksga qo‘shilgan | 2026-08-27 |
DOI: 10.71310/pcam.3_73.2026.10 · Maqolaning asl sahifasi
Falkner–Skan equations, pressure gradient, velocity profile, уравнения Фолкнера–Скэна, градиент давления, профиль скорости
| APA | Тиловов, М.А., & Tilovov, M.A. (2026). Numerical Study of the Dynamics of Derivatives of Various Orders of the Falkner–Skan Equation Depending on the Pressure Gradient. Ҳисоблаш ва амалий математика муаммолари, (3), 139-152. https://doi.org/10.71310/pcam.3_73.2026.10 |
|---|---|
| GOST (OAK) | Тиловов, М.А., Tilovov, M.A. Numerical Study of the Dynamics of Derivatives of Various Orders of the Falkner–Skan Equation Depending on the Pressure Gradient // Ҳисоблаш ва амалий математика муаммолари. – 2026. – № 3. – P. 139-152. – DOI: 10.71310/pcam.3_73.2026.10. |
| MLA | Тиловов, М.А., and Tilovov, M.A. “Numerical Study of the Dynamics of Derivatives of Various Orders of the Falkner–Skan Equation Depending on the Pressure Gradient.” Ҳисоблаш ва амалий математика муаммолари, (3), 139-152, 2026. https://doi.org/10.71310/pcam.3_73.2026.10 |
| Chicago | Тиловов, М.А., and Tilovov, M.A. “Numerical Study of the Dynamics of Derivatives of Various Orders of the Falkner–Skan Equation Depending on the Pressure Gradient.” Ҳисоблаш ва амалий математика муаммолари, (3), 139-152 (2026). https://doi.org/10.71310/pcam.3_73.2026.10 |
| Harvard | Тиловов, М.А., and Tilovov, M.A (2026) ‘Numerical Study of the Dynamics of Derivatives of Various Orders of the Falkner–Skan Equation Depending on the Pressure Gradient’, Ҳисоблаш ва амалий математика муаммолари, (3), 139-152. https://doi.org/10.71310/pcam.3_73.2026.10 |
| BibTeX | @article{article2026,
title = {Numerical Study of the Dynamics of Derivatives of Various Orders of the Falkner–Skan Equation Depending on the Pressure Gradient},
author = {Тиловов, М.А. and Tilovov, M.A.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2026},
number = {3},
pages = {139-152},
doi = {10.71310/pcam.3_73.2026.10},
url = {https://doi.org/10.71310/pcam.3_73.2026.10}
} |
Boshqa maqola uchun iqtibos tayyorlash
This paper presents a three-dimensional numerical study of a novel vertical-axis wind turbine (VAWT) with a unique aerodynamic profile and a passive blade-pitch mechanism. Rectangular blades are mounted on horizontal…
Within a non-conservative formulation of the quasi-one-dimensional linearized mass and momentum conservation equations, transient processes are studied in an elementary undulating pipeline section caused by step-like…
This work presents a comprehensive numerical and analytical study of hydrodynamic and thermal processes in closed pipelines of variable diameter, taking into account terrain relief and external thermal influences. The…
This study presents a mathematical and numerical model for filtration flow, solute transport, adsorption, and membrane fouling in a cylindrical porous filter. The model combines axisymmetric Brinkman–Darcy flow…
The paper addresses the formulation of plane elasticity problems in terms of stresses and their numerical solution by the Galerkin finite element method. Based on the equilibrium equations, geometric relations, and…
This study presents an efficient method for approximating the solutions of a certain class of first-order differential equations with variable coefficients. The approach constructs an auxiliary differential equation…
This paper addresses the development of a mathematical model for evaluating the spatial distribution of fine particulate emissions from a continuous elevated source. The model is built upon the advection-diffusion…
As a devastating fungal disease that seriously threatens potato production, the transmission process of potato early and late blight is significantly affected by environmental fluctuations. To accurately reveal the…
A mathematical model has been developed to provide a more accurate description of atmospheric dust particle transport. Unlike most existing models that assume the particle velocity matches the wind speed, this work…
This study presents a comparative numerical investigation of the Finite Difference Method (FDM) and the Finite Volume Method (FVM) for simulating filtration processes in a cylindrical porous filter. The mathematical…
Ҳисоблаш ва амалий математика муаммолари — barcha maqolalar · 2026-yil arxivi
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…
This article presents the results of 2018-2023, such as biological diversity, inter-landscape distribution characteristics, density,and number of straggly insects identified from natural and anthropogenic areas of…
This article observational data on the species composition, distribution, population, density, and seasonal damage caused causedby herbivorus bugs. Observationes were carried out in April and September 2021. When…
In the article, the research fields of some species belonging to Paeonia, their significance in human life, adaptation features tovarious ecological conditions are highlighted, and the ecologist groups and other…
This article studies the number of species, population density of terrestrial mollusks of the Topalangdarya basin, located in theSurkhandarya region of Uzbekistan, in various altitudinal regions and biotopes and…
This article sheds light on changes in biomass formation and antimicrobial activity against test pathogenic strains under theinfluence of epigenetic modifiers and elicitors of the endophytic fungus Penicillium…
Shahimardonsoy covered issues such as the soil in the river basin and measures to increase its condition, salinity and fertility, theflora and fauna present in the basin landscape and their conservation.