Three-dimensional Linear Hyperbolic System

In the paper, we propose a systematic approach to the development and study of the adequacy of computational models for a mixed dissipative boundary-value problem posed for symmetric t-hyperbolic systems. We consider a three-dimensional linear hyperbolic system with constant coefficients with dissipative boundary conditions. We construct a difference splitting scheme in directions for the numerical calculation of stable solutions for this system.We construct a discrete analogue of the Lyapunov function to study the stability of solutions for the considered problem. We obtain an a priori estimate for this analog, that allows us to state the exponential stability of the numerical solution. Moreover, we prove the theorem on the exponential stability of the solution of a difference splitting scheme for a linear hyperbolic system in Sobolev spaces, which gives us the opportunity to prove the convergence of the numerical solution.