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On Conditions for L2-Dissipativity of Linearized Explicit QGD Finite-Difference Schemes for One-Dimensional Gas Dynamics Equations


An explicit two-level in time and spatially symmetric finite-difference scheme approximating the 1D quasi-gasdynamic system of equations is studied. The scheme is linearized about a constant solution, and new necessary and sufficient conditions for the L2-dissipativity of solutions to the Cauchy problem are derived, including, for the first time, the case of a nonzero background velocity and depending on the Mach number. It is shown that the condition on the Courant number can be made independent of the Mach number. The results provide a substantial development of the well-known stability analysis of the linearized Lax–Wendroff scheme.

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Correspondence to A. A. Zlotnik.

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Original Russian Text © A.A. Zlotnik, T.A. Lomonosov, 2018, published in Doklady Akademii Nauk, 2018, Vol. 482, No. 4.

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Zlotnik, A.A., Lomonosov, T.A. On Conditions for L2-Dissipativity of Linearized Explicit QGD Finite-Difference Schemes for One-Dimensional Gas Dynamics Equations. Dokl. Math. 98, 458–463 (2018).

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