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Re: A simple ordinary differential equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98213] Re: A simple ordinary differential equation
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Fri, 3 Apr 2009 04:32:36 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <gr21kh$lpg$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

what is wrong with

f[x_?NumericQ] = 1 - 1111*x'^2;

?
A derivative x' from a numeric value f[x_?NumericQ]

what is wrong with Sqr[] is it a miss-typed Sqrt[] or is it
a square Sqr[x_]:=x^2


f[x_[t_]] := 1 - 1111*x'[t]^2;
sol = NDSolve[{x''[t] + (16/10^4) x'[t]^2*
        Sqrt[f[x[t]]]/x[t]^2 - (1458/10^9)*f[x[t]]/x[t]^2 == 0,
     x[0] == 1, x'[0] == 0}, {x[t], x'[t]}, {t, 0, 100},
    AccuracyGoal -> 8, PrecisionGoal -> 8, WorkingPrecision -> 30,
    MaxSteps -> Infinity];

and

Plot[Evaluate[x'[t] /. sol], {t, 0, 100}]

work fine.

Regards
   Jens

I. Shechtman wrote:
> What is wrong with this equation?
> 
> Clear[sol]
> f[x_?NumericQ] = 1 - 1111*x'^2;
> sol = NDSolve[{x''[t] + (16/10^4)x'[t]^2*Sqr[
> f[x[t]]]/x[
>     t]^2 - (1458/10^9)*f[x[t]]/x[t]^2 == 
>             0, x[0] == 1, x'[0] == 0}, x[t], {
>               t, 0, 100}, AccuracyGoal -> 8,
>                      PrecisionGoal -> 8, WorkingPrecision -> 
>                   30, MaxSteps -> Infinity];
> Plot[Evaluate[x'[t] /. sol], {t, 0, 100}]
> 


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