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Balakin, V.B. (1970) Methods of the Runge-Kutta Type for Gas Dynamics. USSR Computational Mathematics and Mathematical Physics, 10, 208-216.
https://doi.org/10.1016/0041-5553(70)90192-8

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• TITLE: A Discrete Analogue of Energy Integral for a Difference Scheme for Quasilinear Hyperbolic Systems

  AUTHORS: R. D. Aloev, Z. K. Eshkuvatov, M. U. Khudayberganov, N. M. A. Nik Long

  KEYWORDS: Hyperbolic Systems, Stability, Quasilinear Equations

  JOURNAL NAME: Applied Mathematics, Vol.9 No.7, July 13, 2018

  ABSTRACT: The class of three-dimensional quasilinear hyperbolic systems is studied. The initial boundary value problem for this class of quasilinear hyperbolic systems is given. By constructing the energy’s integral, a priori estimate for the solution of the initial boundary value problem is obtained. Difference scheme is constructed and an a priori estimate for its solution is obtained. Numerical example exhibits the efficiency and accuracy of the method.