Re: How to generate system of 1st order ODE from 2nd order ODEs
- To: mathgroup at smc.vnet.net
- Subject: [mg42574] Re: [mg42561] How to generate system of 1st order ODE from 2nd order ODEs
- From: Selwyn Hollis <selwynh at earthlink.net>
- Date: Wed, 16 Jul 2003 09:13:35 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Rodolfo,
Suppose you have, for example,
sys2 = {y[1]''[x] == y[2][x]y[3]'[x] - y[1]'[x],
y[2]''[x] == y[3][x] - y[1]'[x],
y[3]''[x] == y[1][x] - y[2][x]y[3][x]}
Then this produces the equivalent 1st order system:
sys1 = Join[ Table[y[i]'[x] == v[i][x], {i, 1, 3}],
sys2 /. {y[i_]''[x] -> v[i]'[x], y[i_]'[x] -> v[i][x]} ]
-----
Selwyn Hollis
http://www.math.armstrong.edu/faculty/hollis
On Tuesday, July 15, 2003, at 02:54 AM, Rodolfo Cazabon wrote:
> Greetings everyone...
>
> How might I go about defining rules and patterns such that I can
> define a
> system of 2nd order ODEs and that in turn it symbolically generates the
> equivalent systems of 1st order ODEs.
>
> If anyone might provide me with pointers within the documentation or to
> packages/notebooks that depict how to do this I would truly appreciate
> it.
>
> Sincerely,
> Rodolfo J. Cazabon
> Discreet - a division of Autodesk, Inc.
>
>
>