Сборник статей, посвященный памяти академика Сергея Константиновича Годунова (Под редакцией Ю.Л. Трахинина, М.А. Шишленина)

Summation-by-parts schemes for symmetric hyperbolic systems

Alexander Malyshev

University of Bergen, Department of Mathematics, Postbox 7803, 5020, Bergen, Norway

Аннотация: 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.

Ключевые слова: symmetric hyperbolic system, dissipative boundary conditions, summation-by-parts scheme, simultaneous approximation terms, strong stability of explicit Runge-Kutta methods.

УДК: 519.63

MSC: 65M20

Поступила 1 ноября 2024 г., опубликована 31 декабря 2024 г.

Язык публикации: английский

DOI: 10.33048/semi.2024.21.B07