Summation-by-parts schemes for symmetric hyperbolic systems

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.