Exact boundaries for the analytical approximate solution of a class of first-order nonlinear differential equations in the real domain

Орлов, В. Н.; Kovalchuk, Oleg

doi:10.14498/vsgtu1843

Cited by 2 publications

(1 citation statement)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This paper represents the experimental data obtained by the Department of Hydraulic Engineering and Melioration of the Don State Agrarian University. This work is the development of analytical methods for solving problems of technical mechanics of liquids and gases [1,17,19], using a technique for solving nonlinear problems similar to those proposed in [24][25][26][27][28][29][30].…”

Section: Discussionmentioning

confidence: 99%

Nonlinear Differential Equations of Flow Motion Considering Resistance Forces

Evtushenko,

Kokhanenko,

Burtseva

2023

Axioms

View full text Add to dashboard Cite

For a stationary potential 2D planar open high-velocity water flow of the ideal liquid, we propose a closed system of nonlinear equations considering the resistance forces to the flow from the channel bottom. Tangential stresses on jet interfaces are ignored. The resistance force components are expressed in terms of velocity components. In this case, the flow equations can be solved through the method of characteristics, and the surface forces are reduced to equivalent volumetric forces. The system of non-linear equations is solved in the velocity hodograph plane; further, the transition to the physical plane takes place. Since the value of the hydrodynamic pressure decreases downstream of the flow, the friction forces to the flow in the first approximation can be considered by using the integral laws of resistance. At that, the form of the equations of motion in the plane of the velocity hodograph does not change. This fact is proved in the article. An example of calculating the water flow is provided. The kinecity, ordinates, and velocities of the flow along its extreme line are calculated without considering resistance forces. Validation of the model in the real flow is performed. Acceptable accuracy relative to experimental data is obtained.

show abstract

Section: Discussionmentioning

confidence: 99%

Nonlinear Differential Equations of Flow Motion Considering Resistance Forces

Evtushenko,

Kokhanenko,

Burtseva

2023

Axioms

View full text Add to dashboard Cite

show abstract

The Influence of a Perturbation of a Moving Singular Point on the Structure of an Analytical Approximate Solution of a Class of Third-Order Nonlinear Differential Equations in a Complex Domain

Орлов

Gasanov

2022

HoBMSTU.SNS

View full text Add to dashboard Cite

The authors prove the theorem of existence and uniqueness of the solution, construct an analytical approximate solution in the complex domain for one class of nonlinear differential equations of the third order, the solution of which are discontinuous functions. The solution of the listed mathematical problems is based on the classical approach. Since the existing methods allow obtaining moving singular points only approximately, it is necessary to investigate the effect of a perturbation of a moving singular point on the structure of an analytical approximate solution in the complex domain. Since the existing methods allow obtaining moving singular points only approximately, it is necessary to investigate the effect of a perturbation of a moving singular point on the structure of an analytical approximate solution in the complex domain. A theorem that allows us to determine a priori estimates of the error of the analytical approximate solution is proved. The study applies the classical approach to estimation and illustrates the application of series with fractional negative powers. The article presents the results of numerical experiment confirming the validity of the obtained theoretical position. The technique of optimization of a priori estimates of analytical approximate solution in the vicinity of perturbed value of moving singular point using a posteriori estimates is presented. The results allow expanding the classes of nonlinear differential equations used as a basis for mathematical models of processes and phenomena in various fields of human activity. In particular, the class of equations under consideration can be applied in the study of wave processes in elastic beams, which is confirmed by theoretical data

show abstract

Exact boundaries for the analytical approximate solution of a class of first-order nonlinear differential equations in the real domain

Cited by 2 publications

References 14 publications

Nonlinear Differential Equations of Flow Motion Considering Resistance Forces

Nonlinear Differential Equations of Flow Motion Considering Resistance Forces

The Influence of a Perturbation of a Moving Singular Point on the Structure of an Analytical Approximate Solution of a Class of Third-Order Nonlinear Differential Equations in a Complex Domain

Contact Info

Product

Resources

About