       # 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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