Implicit Upwind Difference Scheme for a Symmetric $$\boldsymbol{t}$$-Hyperbolic System with Variable Coefficients and Lowest Terms

The exponential stability of an upwind implicit difference scheme for a mixed problem posed for linear symmetric $$t$$ -hyperbolic systems with dissipative boundary conditions is proved in this article. The case is considered when the coefficients of a linear symmetric $$t$$ -hyperbolic system are variables and the system involves lowest terms. To solve the initial-boundary value difference problem, an explicit discrete quadratic Lyapunov function is constructed. Boundary conditions were determined, under which the exponential stability of an implicit upwind difference scheme for a mixed problem for linear symmetric $$t$$ -hyperbolic systems with dissipative boundary conditions in the $$l^{2}$$ -norm is proved.

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