  We introduce a new class of Runge-Kutta type methods suitable for time
stepping to propagate hyperbolic solutions within tent-shaped spacetime
regions. Unlike standard Runge-Kutta methods, the new methods yield expected
convergence properties when standard high order spatial (discontinuous
Galerkin) discretizations are used. After presenting a derivation of
nonstandard order conditions for these methods, we show numerical examples of
nonlinear hyperbolic systems to demonstrate the optimal convergence rates. We
also report on the discrete stability properties of these methods applied to
linear hyperbolic equations.
