@TechReport{	  it:2003-023,
  author	= {Bertil Gustafsson and Per Wahlund},
  title		= {Time Compact Difference Methods for Wave Propagation in
		  Discontinuous Media},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2003},
  number	= {2003-023},
  month		= apr,
  abstract	= {In an earlier paper by Gustafsson and Mossberg, a fourth
		  order one-step method was constructed for the solution of
		  wave propagation problems. The method is based on the first
		  order system form of the PDE, and uses a staggered grid
		  both in space and time. The method was also applied with
		  good results to a problem with discontinuous coefficients
		  without using any special procedure across the
		  discontinuity. In this paper we will analyze a model
		  problem from acoustics, and demonstrate the theoretical
		  foundation for this behavior. Furthermore, we shall present
		  more detailed numerical experiments which confirm the
		  theoretical results.}
}