@TechReport{	  it:2011-008,
  author	= {Kenneth Duru and Ken Mattsson and Gunilla Kreiss},
  title		= {Stable and Conservative Time Propagators for Second Order
		  Hyperbolic Systems},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2011},
  number	= {2011-008},
  month		= apr,
  abstract	= {In this paper we construct a hierarchy of arbitrary high
		  (even) order accurate explicit time propagators for
		  semi-discrete second order hyperbolic systems. An accurate
		  semi-discrete problem is obtained by approximating the
		  corresponding spatial derivatives using high order accurate
		  finite difference operators satisfying the summation by
		  parts rule. In order to obtain a strictly stable
		  semi-discrete problem, boundary conditions are imposed
		  weakly using the simultaneous approximation term method.
		  The time discretization starts with a second order central
		  difference scheme, then using the modified equation
		  approach (even in the presence of a first order derivative
		  in time) we derive arbitrary high order accurate time
		  marching schemes. For the fully discrete problem, we
		  introduce a suitable weighted inner product and use the
		  energy method to derive an optimal CFL condition, which
		  provides a useful and rigorous criterion for stability.
		  Numerical examples are also provided. }
}