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We study difference schemes associated with a simplified linearized multidimensionalhyperbolic quasi-gasdynamic system of differential equations. It is shown that an explicit two-levelvector difference scheme with flux relaxation for a second-order hyperbolic equation with variablecoefficients that is a perturbation of the transport equation with a parameter multiplying thehighest derivatives can be reduced to an explicit three-level difference scheme. In the case ofconstant coefficients, the spectral condition for the time-uniform stability of this explicitthree-level difference scheme is analyzed, and both sufficient and necessary conditions for thiscondition to hold are derived, in particular, in the form of Courant type conditions on the ratio oftemporal and spatial steps.

Spectral Stability Conditions for an Explicit Three-Level Finite-Difference Scheme for a Multidimensional Transport Equation with Perturbations