scholarly journals Modeling and automation processes of water purification from multicomponent pollution

2019 ◽  
pp. 64-66
Author(s):  
Andrii Safonyk ◽  
Olga Safonyk ◽  
Victoria Zhabchyk
Keyword(s):  
Mass Transfer ◽  
Mathematical Models ◽  
Boundary Value Problems ◽  
Water Purification ◽  
Boundary Value ◽  
Asymptotic Methods ◽  
Singularly Perturbed ◽  
Diffusion Mass Transfer ◽  
Automation Systems ◽  
Diffusion Mass

Mathematical models of the processes of cleaning liquids from multicomponent contamination by filtration, as well as diffusion-mass transfer perturbations and the development of numerical-asymptotic methods for solving the corresponding nonlinear regularly and singularly perturbed boundary value problems are shown. The construction of automation systems of corresponding treatment systems and complexes on the basis of solving model problems is presented.

scholarly journals Asymptotic methods for solving boundary value eigenvalue problems

2020 ◽  
Vol 164 ◽  
pp. 09022
Author(s):  
Galina Zhukova
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Numerical Integration ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Asymptotic Methods ◽  
Singularly Perturbed ◽  
Asymptotic Behavior Of Solutions ◽  
Diagram Method

The aim of the study is an approximate construction with a given accuracy of solutions of boundary value problems for eigenvalues under various types of boundary conditions. It is shown that the problem of finding approximate large eigenvalues of boundary value problems is reduced to the analysis and solution of singularly perturbed differential equations with variable coefficients. Methods used: asymptotic diagram method developed to construct the asymptotic behavior of solutions of singularly perturbed differential equations and systems; methods of numerical integration of boundary value problems. The main results obtained are: the asymptotics of the required accuracy are constructed in the analytical form for the eigenvalues and eigenfunctions of the boundary value problems under various boundary conditions; analysis of the computational capabilities of the practical use of the constructed asymptotics in comparison with the results of numerical integration.

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