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 Kindybaliuk Arkadii, Prytula M.
Name of the article Direct method of Lie-algebraic discrete approximations for advection equation
Abstract We propose the direct method of Lie-algebraic discrete approximation for numerical solving the Cauchy problem for advection equation in this paper. Discretization of the equation is performed by means of the Lie-algebraic quasi representations for space variables of the equation and by means of Taylor series expansion and small parameter method for the time variable. Such combination of approaches leads to a factorial rate of convergence with respect to all variables in the equation if the quasi representations for differential operator are built by means of Lagrange interpolation. The approximation properties and error estimations for the proposed scheme are investigated. The factorial rate of convergence for the proposed numerical scheme has been proven.
Language English
PDF format Kindybaliuk Arkadii, Prytula M. 
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