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Regular version of the site

Article

Stability of implicit difference schemes for a linearized hyperbolic quasi-gasdynamic system of equations

Differential Equations. 2020. Vol. 56. No. 7. P. 910-922.
Zlotnik A.A., Chetverushkin B.

We consider a multidimensional hyperbolic quasi-gasdynamic system of differential equations of the second order in time and space linearized at a constant solution (with an arbitrary velocity). For the linearized system with constant coefficients, we study an implicit three-level weighted difference scheme and an implicit two-level vector difference scheme. The important domination property of the operator of viscous terms 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 of the initial–boundary value problem uniformly in time and the relaxation parameter.