@TechReport{	  it:2004-040,
  author	= {Magnus Sv{\"a}rd and Jan Nordstr{\"o}m},
  title		= {On the Order of Accuracy for Difference Approximations of
		  Initial-Boundary Value Problems},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2004},
  number	= {2004-040},
  month		= sep,
  abstract	= {Finite difference approximations of the second derivative
		  in space appearing in, parabolic, incompletely parabolic
		  systems of, and second order hyperbolic, partial
		  differential equations are considered. If the solution is
		  pointwise bounded, we prove that finite difference
		  approximations of those classes of equations can be closed
		  with two orders less accuracy at the boundary without
		  reducing the global order of accuracy.
		  
		  This result is generalised to initial-boundary value
		  problems with an $m$th order principal part. Then, the
		  boundary accuracy can be lowered $m$ orders.
		  
		  Further, it is shown that summation-by-parts operators with
		  approximating second derivatives are pointwise bounded.
		  Linear and nonlinear computations corroborates the
		  theoretical results.}
}