# Re: Numerical Solution to a System of Differential Equations...

• To: mathgroup@smc.vnet.net
• Subject: [mg12233] Re: Numerical Solution to a System of Differential Equations...
• From: Paul Abbott <paul@physics.uwa.edu.au>
• Date: Tue, 5 May 1998 03:29:30 -0400
• Organization: University of Western Australia
• References: <6ibvba\$ev@smc.vnet.net>

```Ragavan wrote:

> Now, I try to solve using NDSolve:
>
>         y, {t,0,10}]

You could just write

NDSolve[{Thread[y' == M . y], Thread[y0 == Init]}, y, {t, 0, 10}]

> and obtain an output which looks like this:
>
> Out[4]={y1[t]\[Rule]InterpolatingFunction[{{0.`,10.`}},"<>"][t],
>         y2[t]\[Rule]InterpolatingFunction[{{0.`,10.`}},"<>"][t],
>         y3[t]\[Rule]InterpolatingFunction[{{0.`,10.`}},"<>"][t]}}
>
> (y1, y2, y3 are elements in the y vector.)

y = {y1[t],y2[t],y3[t],y4[t]}

for otherwise NDSolve would return

{y1\[Rule]InterpolatingFunction[{{0.`,10.`}},"<>"], ...

> But when I try to look at the result for a given value of the dependent
> variable t (say 5):
>
> In[5]:= y3[5] /. %
>
> all I get is
>
> Out[5]= y3[5]

This is because the replacement rule is for y1[t] not for y1.  Here is
one way to get what you want:

y = {y1, y2, y3, y4};

NDSolve[{Thread[D[Through[y[t]], t] == M . Through[y[t]]],
Thread[Through[y[0]] == Init]}, y, {t, 0, 10}]

{{y1 -> InterpolatingFunction[],
y2 -> InterpolatingFunction[],
y3 -> InterpolatingFunction[],
y4 -> InterpolatingFunction[]}}

Cheers,
Paul

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907
mailto:paul@physics.uwa.edu.au  AUSTRALIA
http://www.pd.uwa.edu.au/~paul

God IS a weakly left-handed dice player
____________________________________________________________________

```

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