Stability of Implicit Difference Schemes for a Linearized Hyperbolic Quasi-Gasdynamic System of Equations

We consider a multidimensional hyperbolic quasi-gasdynamic system of differential equations of the second order in time and space linearized on a constant solution (with an arbitrary velocity). For the linearized system with constant coefficients, we study the implicit three-level weighted and two-level vector difference schemes. The important domination property of the operator of viscous terms (with no allowance for the relaxation parameter) over the operator of convective terms is derived. We apply this property to prove by the energy method that, regardless of the Mach number, our implicit schemes on a nonuniform rectangular mesh (without any conditions on the mesh steps) are stable with respect to the initial data and the right-hand side uniformly in time and the relaxation parameter.