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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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