@TechReport{	  it:2008-005,
  author	= {Stefan Engblom},
  title		= {A Discrete Spectral Method for the Chemical Master
		  Equation},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2008},
  number	= {2008-005},
  month		= feb,
  note		= {Supersedes report nr 2006-036. Updated Feb 29, 2008.},
  abstract	= {As an equivalent formulation of the Markov-assumption of
		  stochastic processes, the master equation of chemical
		  reactions is an accurate description of general systems in
		  chemistry. For $D$ reacting species this is a
		  differential-difference equation in $D$ dimensions, exactly
		  soluble for very simple systems only.
		  
		  We present and analyze a novel solution strategy based upon
		  a Galerkin spectral method with an inherent natural
		  adaptivity and a very favorable choice of basis functions.
		  
		  The method is demonstrated by the numerical solution of two
		  model problems followed by two more realistic systems taken
		  from molecular biology. It is shown that the method remains
		  effective and accurate, providing a viable alternative to
		  other solution methods when the dimensionality is not too
		  high.}
}