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MathGroup Archive 2004

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How to express ODE?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52817] How to express ODE?
  • From: Adam Getchell <agetchell at physics.ucdavis.edu>
  • Date: Mon, 13 Dec 2004 04:24:15 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Still (unfortunately) not getting another ODE to work, even using Dr. 
Bob's example. I want to express this equation:

In[143]:=
m = 10^16;
mp = 1.2211*10^19;
G = mp^(-2);
V[\[Phi]_] := (1/2)*m^2*\[Phi][t]
\[Rho][\[Phi]_] :=
  Derivative[1][\[Phi]][t]^2/2 +
   V[\[Phi]]
H := Sqrt[((8*Pi*G)/3)*
    \[Rho][\[Phi]]]

In[149]:=
Inflaton :=
  Derivative[2][\[Phi]][t] +
   3*H*Derivative[1][\[Phi]][
     t] + D[V[\[Phi]], \[Phi]]

That is, phi double-dot of t + 3 H phi dot of t + V' of phi, where phi 
is a function of t; V is a function of phi; H is a function of rho; rho 
is a function of phi dot and V.

However, solving Inflaton for phi as a function of t:

In[163]:=
f = \[Phi] /. First[NDSolve[
     {Inflaton == 0,
      Derivative[1][\[Phi]][
        t] == 0}, \[Phi],
     {t, 0, 100*m}]]

Generates NDSolve::overdet and ReplaceAll::reps.

I *think* part of my problem is that dV/d(phi) is not getting properly 
evaluated (it returns 0 when I look at it explicitly).

I thought that Derivative[1][\[Phi]][x] would give the above, but not 
the way I'm doing it.

--Adam


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