Geodesic
Summation-by-parts schemes for symmetric hyperbolic systems
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. B92-B125 Cet article a éte moissonné depuis la source Math-Net.Ru

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We apply the method of lines to numerically solve general initial-boundary value problems for symmetric hyperbolic systems of linear differential equations with variable coefficients. Semi-discretization of symmetric hyperbolic systems is performed using classical summation-by-parts difference operators. Strictly dissipative boundary conditions are weakly enforced using the so-called simultaneous approximation terms. All theoretical constructions are provided with full proofs. The stability of explicit Runge-Kutta methods for semi-bounded operators is proved using recent results on strong stability for semi-dissipative operators.
Keywords: symmetric hyperbolic system, dissipative boundary conditions, summation-by-parts scheme, simultaneous approximation terms, strong stability of explicit Runge-Kutta methods. 
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Alexander Malyshev. Summation-by-parts schemes for symmetric hyperbolic systems. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. B92-B125. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a75/

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