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Re: matrix differential equations with NDSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg40264] Re: matrix differential equations with NDSolve
• From: guillerm at aida.usal.es (Guillermo Sanchez)
• Date: Fri, 28 Mar 2003 04:32:13 -0500 (EST)
• References: <b5up59$lmf$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

You can download (http://web.usal.es/~guillerm/biokmod.htm) my package
Biokmod for Solving SODE using Matrix Notation

Guillermo

Selwyn Hollis <selwynh at earthlink.net> wrote in message news:<b5up59$lmf$1 at smc.vnet.net>...
> 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
> >