A comparison is made of finite-difference schemes with the exact solution of a parabolic partial differential equation. A stability analysis
has also been carried out. To solve the parabolic equation, one-step and twostep finite-difference methods are used.
The article discusses the mathematical modeling of the movement of viscous incompressible fluids through a bundle of tubes
located inside the outer pipe. The laminar and turbulent modes of this movement are considered, and the physical meaning of their occurrence is also analyzed. The fluid flow through n tubes of length L and radius r located inside the outer tube is considered. Calculation formulas are derived for calculating the maximum velocity of this flow, the volume of fluid passing through the cross section of the tube, the coefficient of resistance to friction in the tube along the length of the flow, and also the maximum value of the tangential stress. The results of the study of the relationship of the coefficient of resistance to friction in the tube with the Reynolds number are presented. A description is given of a device created according to the results of a study that brings the disordered flow of liquids into a laminar state