Re: solving for variable and then get these e's..?

• To: mathgroup at smc.vnet.net
• Subject: [mg46945] Re: solving for variable and then get these e's..?
• From: sean_incali at yahoo.com (sean kim)
• Date: Tue, 16 Mar 2004 19:55:11 -0500 (EST)
• References: <c33de2\$ftc\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```ok. i see my mistake now.

now that's been solved. now I have solve routine bringing back numbers
like...

{{y[0] == -0.4018557514460829 - 1.486847345781845*I,
x[0] == 0.5 + 1.8499764410878863*I,
z[0] == 0.2124216262618104 + 0.78595000832385*I},
{y[0] == -0.4018557514460829 + 1.486847345781845*I,
x[0] == 0.5 - 1.849976441087886*I,
z[0] == 0.2124216262618104 - 0.7859500083238501*I}}

what does that mean?  why all those imagiinary numbers?  is that
correct?  and Chop doesn't get rid of them.  maybe they are actual
solutions?

sean_incali at yahoo.com (sean kim) wrote in message news:<c33de2\$ftc\$1 at smc.vnet.net>...
> Hello Group.
>
> I was playing around with lorenz system again. I assigned random
> numbers for all the parameters. and made a steady state system based
> on that and solved for the variables. and I get the following. ( the
> code is at the bottom)
>
> {y[0] == 0.1889025652295933*(-1.3382047869208344 -
>      0.47590327034877034*Sqrt[7.906927918602607 -
>         18.515309886236974*e]),
>   x[0] == 0.31792235868739005*(1.5727110293983604 +
>      0.5593002876087739*Sqrt[7.906927918602607 -
>         18.515309886236974*e]),
>   z[0] == 0.042970475451898735*(7.906927918602607 +
>      2.8119260158479644*Sqrt[7.906927918602607 -
>         18.515309886236974*e]}
>
> What are those little e's at the end of the solutions? Is that euler's
> number? and why can't I use that in NDSolve routine? are those
> signifcant?
>
> any thoughts are appreciated.
>
> In[270]:=
> ode = {x'[t]== -a y[t]-b z[t],y'[t]== c x[t]+d y[t],
>     z'[t] == e-f z[t]+f x[t] z[t]}
>
> %/._'[t]->0
>
> Solve[%,{x[t], y[t], z[t]}]
>
> %/.{a-> Random[Real, {1, 3}], b-> Random[Real, {1, 3}],
> c-> Random[Real, {1, 3}],d-> Random[Real, {1, 3}],
> d-> Random[Real, {1, 3}],f-> Random[Real, {1, 3}]}/.Rule ->Equal/.t->
> 0 //InputForm
>
> s1 =% [[1]]
> s2 = %%[[2]]
>
> NDSolve[Join[{x'[t]\[Equal]-a y[t]-b z[t],y'[t]\[Equal]c x[t]+d y[t],
>       z'[t]\[Equal]e-f z[t]+f x[t] z[t]}, s1], {x[t], y[t], z[t]}, {t,
> 0, 10}]

```

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