An algebraic condition for the exponential stability of an upwind difference scheme for hyperbolic systems

In the paper, we investigate the question of obtaining the algebraic condition for the exponential stability of the numerical solution of the upwind difference scheme for the mixed problem posed for one-dimensional symmetric $t$-hyperbolic systems with constant coefficients and with dissipative boundary conditions. An a priori estimate for the numerical solution of the boundary-value difference problem is obtained. This estimate allows us to state the exponential stability of the numerical solution. A theorem on the exponential stability of the numerical solution of the boundary-value difference problem is proved. Easily verifiable algebraic conditions for the exponential stability of the numerical solution are given. The convergence of the numerical solution is proved.