Re: matrix differential equations with NDSolve
- To: mathgroup at smc.vnet.net
- Subject: [mg40241] Re: [mg40220] matrix differential equations with NDSolve
- From: Selwyn Hollis <selwynh at earthlink.net>
- Date: Thu, 27 Mar 2003 06:50:26 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
You do need to provide DSolve and NDSolve with a list containing the
individual equations, but that can be obtained fairly easily. Here's a
simple 2x2 example.
a:= {{1, -2}, {-2, -1}}; initialvals := {1,2};
Y[t_] = Table[y[i][t], {i, Length[a]}]
{y[1][t], y[2][t]}
deqns = Thread[Y'[t] == a.Y[t]]
{y[1]'[t] == y[1][t] - 2*y[2][t], y[2]'[t]
== -2*y[1][t] - y[2][t]}
ics = Thread[Y[0] == initialvals]
{y[1][0] == 1, y[2][0] == 2}
ivp = Flatten[{eqns, ics}]
{y[1]'[t] == y[1][t] - 2*y[2][t], y[2]'[t] ==
-2*y[1][t] - y[2][t], y[1][0] == 1, y[2][0] == 2}
Now you can either
DSolve[ivp, Y[t], t]
or
NDSolve[ivp, Y[t], {t, 0, 1}]
-----
Selwyn Hollis
http://www.math.armstrong.edu/faculty/hollis
On Wednesday, March 26, 2003, at 02:42 AM, Richard Easther wrote:
> Is there an easy way to solve matrix (ordinary) differential equations
> numerically inside of Mathematica? (The hard way is to spell them out
> term by term, of course)
>
> It may be I am missing something obvious, but a quick set of
> experiments with NDSolve did not bring any joy....
>
> Richard Easther
>