@TechReport{	  it:2003-040,
  author	= {Wendy Kress},
  title		= {Error Estimates for Deferred Correction Methods in Time},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2003},
  number	= {2003-040},
  month		= aug,
  abstract	= {In this paper, we consider the deferred correction
		  principle for high order accurate time discretization of
		  partial differential equations (PDEs) and ordinary
		  differential equations (ODEs). Deferred correction is based
		  on a lower order method, here we use second order accurate
		  A-stable methods. Solutions of higher order accuracy are
		  computed successively. The computational complexity for
		  calculating higher order solutions is comparable to the
		  complexity of the lower order method. There is no stability
		  restraint on the size of the time-step. Error estimates are
		  derived and the application of the schemes to initial
		  boundary value problems is discussed in detail. The
		  theoretical results are supported by a series of numerical
		  experiments.}
}