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MathGroup Archive 2004

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46911] solving for variable and then get these e's..?
  • From: sean_incali at yahoo.com (sean kim)
  • Date: Sun, 14 Mar 2004 23:54:26 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

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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