Stability conditions of the upwind scheme for linear hyperbolic systems in the non

Аннотация

The article is devoted to 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 in the non uniform case when the characteristic speeds depend on a spatial variable. An a priori estimate for a numerical solution of the boundary value difference problem is obtained. This estimate allows us to state the exponential stability of the numerical solution. Exponential stability theorems are proved and easily verifiable algebraic conditions of exponential stability are given both for a solution of the differential problem and numerical solution of the boundary value difference problem.