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MathGroup Archive 2004

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Re: How to express ODE?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52831] Re: How to express ODE?
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 14 Dec 2004 05:59:27 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <cpjr25$nvl$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

a) if V[phi] generate a function phi[t] you has to build the derivative
   with respect to phi[t] and not with respect to phi only
b) the parameters are extrem bad scaled for numerical work and you should 
rescale
   it.
c) Your input say

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

that phi'[t] (for all t) is zero, and so phi[t] can be only a constant

d) you have missed the initial conditions for phi[0] and phi'[0] and
   NDSolve[] can't work with out that.

e) until you don't proper scale the parameters and the variables
   NDSolve[] will need a very long time to compute the solution
   with the given accuracy

Regards
 Jens

"Adam Getchell" <agetchell at physics.ucdavis.edu> schrieb im Newsbeitrag 
news:cpjr25$nvl$1 at smc.vnet.net...
> 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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