Stability investigation of an implicit difference scheme for a nonlinear transport equation
https://doi.org/10.29235/1561-2430-2023-59-4-279-290
Abstract
In this paper, we investigate the stability with respect to initial data in the uniform norm of an implicit difference scheme approximating a nonlinear transport equation. An iterative process is used to implement the difference scheme. The convergence of the iterative process and the stability of the difference scheme are proven in the case of initial data guaranteeing the absence of shock waves. In the case of the occurrence of shock waves, estimates of the growth of spatial derivatives at each time layer are obtained. An adaptive computational algorithm for solving the transfer equation during the formation of shock waves is built.
About the Authors
M. M. Chuiko
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Mikhail M. Chuiko – Ph. D. (Physics and Mathematics), Leading Researcher of the Department of Computational Mathematics
11, Surganov Str., 220072, Minsk, Republic of Belarus
O. M. Korolyova
Belarusian National Technical University
Belarus
Belarus
Olga M. Korolyova – Ph. D. (Physics and Mathematics), Associate Professor of the Department of Higher Mathematics,
65, Nezalezhnosti Ave., 220013, Minsk, Republic of Belarus
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