@TechReport{	  it:2006-036,
  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		= {2006},
  number	= {2006-036},
  month		= jun,
  note		= {Superseded by report nr 2008-005},
  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 in the
		  form of a Galerkin spectral method with an inherent natural
		  adaptivity and a very favorable choice of basis functions.
		  
		  The method is exemplified by the numerical solution of two
		  systems taken from molecular biology. It is shown that the
		  method remains effective and accurate when other
		  traditional solution methods produce less useful results.
		  }
}