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Re: Re: Solving Ordinary differential equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105030] Re: [mg104981] Re: [mg104962] Solving Ordinary differential equations
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Wed, 18 Nov 2009 06:59:57 -0500 (EST)
  • References: <20091115085120.UOAZJ.966245.imail@eastrmwml47>
  • Reply-to: drmajorbob at yahoo.com

No, THAT code doesn't work... but this code does:

d = 2*10^-2;
A = d^2 Pi/4;
Po = 5*101325;
Pa = 1*101325;
rho = 1000;
V0 = 5*10^-3;
gamma = 114/100;
sol = V /.
    NDSolve[{V'[t] == A Sqrt[2 (Po (V0/V[t])^gamma - Pa)/rho],
       V[0] == V0}, {V}, {t, 0, 9}, MaxSteps -> 1000000,
      AccuracyGoal -> 10, PrecisionGoal -> 10][[1]];
v[t_] := Chop[sol[t]]
Plot[v[t]*1000, {t, 0, 9}, PlotRange -> All]
Grid[Table[{t, v[t]}, {t, 0, 9, 1}]]

Do you not see the difference? For instance,

d = 2*10^-2

1/50

is very different from your

d = 2*10 - 2

18

Bobby

On Sun, 15 Nov 2009 19:48:35 -0600, Matteo <matteo.diplomacy at gmail.com>  
wrote:

> So..you suggest to modify in this way my code:
>
> d = 2*10 - 2;
> A = d^2 Pi/4;
> Po = 5*101325;
> Pa = 1*101325;
> rho = 1000;
> V0 = 5*10 - 3;
> gamma = 114/100;
> sol = V /.
>    NDSolve[{V'[t] == A Sqrt[2 (Po (V0/V[t])^gamma - Pa)/rho],
>       V[0] == V0}, {V}, {t, 0, 9}, MaxSteps -> 1000000,
>      AccuracyGoal -> 10, PrecisionGoal -> 10][[1]];
> v[t_] := Chop[sol[t]]
> Plot[v[t]*1000, {t, 0, 9}, PlotRange -> All]
> Grid[Table[{t, v[t]}, {t, 0, 9, 1}]]
>
> Does it run on you machine?
> I get this error message:
>
> DSolve::mxst: Maximum number of 1000000 steps reached at the point t ==  
> 0.0789357392769894`.
>
> I tried to set up MaxStep -> 10^7 but the new error is
>
>
> DSolve::mxst: Maximum number of 1000000 steps reached at the point t ==  
> 0.11680804227781108`.
>
>
> I had the problem to have imaginary part for variables that I know it  
> must be real.
> I would solve my trouble definitively by this example-problem.
>
>
>
> Bob Hanlon ha scritto:
>> It makes no sense to enter Pi to two decimal places. In general, enter  
>> all constants exactly and let the subsequent processes define the  
>> overall precision.
>>
>> d = 2*10^-2;
>> A = d^2 Pi/4;
>> Po = 5*101325;
>> Pa = 1*101325;
>> rho = 1000;
>> V0 = 5*10^-3;
>> gamma = 114/100;
>>
>> sol = V /. NDSolve[{
>>       V'[t] == A Sqrt[2 (Po (V0/V[t])^gamma - Pa)/rho],
>>       V[0] == V0}, {V}, {t, 0, 9},
>>      MaxSteps -> 1000000,
>>      AccuracyGoal -> 10,
>>      PrecisionGoal -> 10][[1]];
>>
>> Use Chop to eliminate the numeric noise (imaginary values smaller than  
>> your accuracy and precision).
>>
>> v[t_] := Chop[sol[t]]
>>
>> Plot[v[t]*1000, {t, 0, 9},
>>  PlotRange -> All]
>>
>> Grid[Table[{t, v[t]}, {t, 0, 9, 1}]]
>>
>>
>> Bob Hanlon
>>
>> ---- Allamarein <matteo.diplomacy at gmail.com> wrote:
>>
>> =============
>> I'd solve this ODE:
>>
>> V'[t] == A Sqrt[2 (Po (V0/V[t])^gamma - Pa)/rho
>> IC: V[0] == V0
>>
>> I wrote this code:
>>
>> d = 2*10^-2 ;
>> A = d^2  3.14/4;
>> Po = 5 *101325;
>> Pa = 1*101325 ;
>> rho = 1000 ;
>> V0 = 5*10^-3 ;
>> gamma = 1.14;
>> sol = NDSolve[{
>>     V'[t] == A Sqrt[2 (Po (V0/V[t])^gamma - Pa)/ rho],
>>     V[0] == V0},
>>    {V}, {t, 0, 9},
>>    MaxSteps -> 1000000, AccuracyGoal -> 10, PrecisionGoal -> 10];
>> v[t_] := V[t] /. sol[[1]];
>> Plot[Evaluate[V[t] /. sol]*1000, {t, 0, 9}, PlotRange -> All]
>> Grid[Table[{t, v[t]}, {t, 0, 9, 1}]]
>>
>> If it can be useful, I can underline units of these variables:
>> d [m]
>> P0, Pa [Pa]
>> rho [kg/m^3]
>> V [m^3]
>> gamma [--]
>> t [sec]
>>
>> Running this code, V has got comlex part. This is impossible, because
>> it's a volume.
>> I should re-write my ODE in order NDSolve can digest better or I can
>> set an option in my code where I suggest " V must be positive and
>> real"?
>>
>>
>>
>


-- 
DrMajorBob at yahoo.com


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