Difference upwind scheme for the numerical calculation of stable solutions for a linear hyperbolic system

In this article, the stability of the difference upwind scheme for the numerical calculation of stable solutions of the mixed dissipative boundary value problem for a linear hyperbolic system of two equations is studied. A discrete analogue of the Lyapunov function is constructed for the numerical values of stable solutions. An a priori estimate is obtained for a discrete analog of the Lyapunov function. Theorems on the exponential stability of the solution of both the differential problem and the difference scheme in the corresponding norms are proved.

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