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Re: A simple ordinary differential equation

• To: mathgroup at smc.vnet.net
• Subject: [mg98211] Re: [mg98201] A simple ordinary differential equation
• From: "Pasha Karami" <karami at geo.uu.nl>
• Date: Fri, 3 Apr 2009 04:32:14 -0500 (EST)
• References: <200904020948.EAA22322@smc.vnet.net>

Hi,

I think you are doing few mistakes:
1) you miss "t" in the Sqrt function
2) you define a function f as a function of x which does not include t.
Better not to do that ans simply put this term in your equations; but
check it first if I am right.
3)You solve equations for x[t] but you plot for x'[t]. Since it is
numerically solve better to solve equations for x'[t].

I have the modified code below but not sure if it is really true. Please
check it first.
Clear[sol]
sol = NDSolve[{x''[t] + (16/10^4) x'[t]^2*
       Sqrt[(1 - 1111*x'[t]^2)]/
        x[t]^2 - (1458/10^9)*(1 - 1111*x'[t]^2)/x[t]^2 == 0,
    x[0] == 1, x'[0] == 0}, x'[t], {t, 0, 100}, AccuracyGoal -> 0,
   PrecisionGoal -> 0, MaxSteps -> Infinity];
Plot[Evaluate[x'[t] /. sol], {t, 0, 100}]

Regards,
Pasha



> 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}]
>
>


PhD student "Pasha Karami"
Room z.206,Dept. of Earth Sciences
Utrecht University
Budapestlaan 4
3584 CD Utrecht
The Netherlands
Tel:+31-30-2537503

• References:
  • A simple ordinary differential equation
    • From: "I. Shechtman" <shechtma@netvision.net.il>