Scientific publications of the Ivan Franko National University of Lviv

Visnyk of the Lviv University. Series Applied Mathematics and Computer Science

Additional information
Year 2018
Volume 26
Authors Venherskyi P., Kokovska Y., Trushevskyi V.
Name of the article Application of different approaches to the solution of the problem of chanell water flow in kinematic approximation
Abstract It is shown how from the general equations of channel flow of water in hydrodynamic formulation, the equations of channel flow of water are obtained in the kinematic approximation. A variational statement of the channel flow problem was constructed to find unknown values of the cross-sectional area of channel flows at an arbitrary time point. A numerical scheme for solving variational problems using the finite element method (FEM) and one-time recurrent integration schemes in time has been developed. The stability and analysis of the convergence of the constructed numerical schemes by the analysis of the corresponding energy norms is proved.
An alternative approach to solving the problem of channel flow of water, based on the implementation of the projection grid scheme of the finite element method on a recurrent artificial neural network, is considered. Efficiency of application for this task of a neural network on the basis of radial basis functions (RBF) is investigated. The RBF network is constructed on the basis of multidirectional basis functions. Learning the network is to minimize the resulting functional error. This approach can be effectively applied to solving nonlinear problems of channel flow of water.
Language Ukrainian
PDF format Venherskyi P., Kokovska Y., Trushevskyi V. 
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