Numerical Study of the Dynamics of Derivatives of Various Orders of the Falkner–Skan Equation Depending on the Pressure Gradient
DOI:
https://doi.org/10.71310/pcam.3_73.2026.10Keywords:
Falkner–Skan equations, pressure gradient, velocity profileAbstract
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.
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