On L^2-dissipativity of linearized explicit finite-difference schemes with a regularization on a non-uniform spatial mesh for the 1D gas dynamics equations
We deal with an explicit finite-difference scheme with a regularization for the 1D gas dynamics equations linearized at the constant solution. The sufficient condition on the Courant number for the $L^2$-dissipativity of the scheme is derived in the case of the Cauchy problem and a non-uniform spatial mesh. The energy-type technique is developed to this end, and the proof is both short and under clear conditions on matrices of the convective and regularizing (dissipative) terms. A scheme with a kinetically motivated regularization is considered as an application in more detail.