Collection of papers in honor of Sergey Godunov (Editors: Yu. L. Trakhinin, M.A. Shishlenin)

Summation-by-parts schemes for symmetric hyperbolic systems

Alexander Malyshev

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

Abstract: 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.

UDC: 519.63

MSC: 65M20

Received November 1, 2024, published December 31, 2024

Language: English

DOI: 10.33048/semi.2024.21.B07