Stability with respect to coefficients of solution of difference schemes approximating initial boundary-value problems for semi-linear hyperbolic equations
https://doi.org/10.29235/1561-8323-2020-64-2-135-143
Abstract
The stability with respect to coefficients of solution of a difference scheme approximating the initial boundary-value problem for the one-dimensional semi-linear hyperbolic equation is studied. The estimates of the solutions of both differential and difference problems are obtained. In the domain of existence of the solution, the estimates for perturbation of the solution of a difference scheme with respect to perturbation of the coefficients of the equation are obtained. These estimates are consistent with the estimates for the differential problem. In all cases, the method of energy inequalities, the Bihari inequality and its mesh analogue are used.
About the Authors
P. P. Matus
John Paul II Catholic University of Lublin, Poland; Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Matus Piotr P. – Corresponding Member, D. Sc. (Physics and Mathematics), Professor, Chief Researcher.
11, Surganov Str., 220072, MinskS. V. Lemeshevsky
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Lemeshevsky Sergey V. – Ph. D. (Physics and Mathematics), Director.
11, Surganov Str., 220072, MinskReferences
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