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}]