@TechReport{	  it:2000-026,
  author	= {Henrik Brand{\'e}n},
  title		= {Numerical Boundary Conditions for {ODE}},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2000},
  number	= {2000-026},
  month		= oct,
  optnote	= {Submitted to Numerische Mathematik},
  abstract	= {We consider consistent finite difference approximations of
		  ordinary differential equations, and in particular,
		  parasitic solutions. A framework is introduced,
		  representing a discrete solution as a sum of the true
		  solution and a number of parasitic solutions. We show that
		  within this framework, finite difference equations can be
		  analysed using theory of ordinary differential equations,
		  simplifying the analysis considerably. As an example we
		  give a simple recipe on how to construct numerical boundary
		  conditions such that the solution converges with expected
		  accuracy.}
}