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MathGroup Archive 1998

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writing out a general n-th order iterative eqn.


  • To: mathgroup@smc.vnet.net
  • Subject: [mg10323] writing out a general n-th order iterative eqn.
  • From: ngrjn@u.washington.edu (V. Nagarajan)
  • Date: Thu, 8 Jan 1998 23:40:48 -0500
  • Organization: University of Washington, Seattle


	I would appreciate someone pointing me in the right
	direction.

	I have an n-th order eqn.,

	{rho^(n) (t)}ij = {A(t)}ij (x) {B(t).rho^(n-1) - rho^(n-1).B(t)}ij

	^ = superscript
	{..}ij = ij-th matrix element
	. = scalar multiplication


	The equation gets quite tedious upon substituting for the lower
	order successively because {x.y}ij = Sum(k=1,N)({x}ik.{y}kl).
	For N=2 and n=3, i can express rho^(3) as a function of rho^(0)
	fairly easily. It is when these integers get to be larger,
	the bookkeeping gets to be horrendous.

	I am looking to use Mathematica, if possible, to express higher
	order rho as a function of rho^(0).

	It seems to me that since the equation can be iterated methodically,
	I should be able to use the symbolic aspect of Mathematica
	to write out all the terms. I have looked into the function Nest,
	but the convolution makes its application not straightforward
	at the least.

	Where can i find out more?

	Thanks in advance for all info.

							- Nagarajan




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