       Re: Re: Solving Ordinary differential equations

• To: mathgroup at smc.vnet.net
• Subject: [mg105040] Re: [mg104981] Re: [mg104962] Solving Ordinary differential equations
• From: Matteo <matteo.diplomacy at gmail.com>
• Date: Thu, 19 Nov 2009 05:21:15 -0500 (EST)
• References: <20091115085120.UOAZJ.966245.imail@eastrmwml47> <200911160148.UAA06805@smc.vnet.net> <op.u3kp1qhrtgfoz2@bobbys-imac.local>

```Yeah...silly error to copy my code.
Thanks.

DrMajorBob ha scritto:
> 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 == V0}, {V}, {t, 0, 9}, MaxSteps -> 1000000,
>      AccuracyGoal -> 10, PrecisionGoal -> 10][];
> 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 == V0}, {V}, {t, 0, 9}, MaxSteps -> 1000000,
>>      AccuracyGoal -> 10, PrecisionGoal -> 10][];
>> 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 == V0}, {V}, {t, 0, 9},
>>>      MaxSteps -> 1000000,
>>>      AccuracyGoal -> 10,
>>>      PrecisionGoal -> 10][];
>>>
>>> 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 == 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 == V0},
>>>    {V}, {t, 0, 9},
>>>    MaxSteps -> 1000000, AccuracyGoal -> 10, PrecisionGoal -> 10];
>>> v[t_] := V[t] /. sol[];
>>> 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"?
>>>
>>>
>>>
>>
>
>

```

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