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[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"? >>> >>> >>> >> > >

**References**:**Re: Solving Ordinary differential equations by NDSolve***From:*Matteo <matteo.diplomacy@gmail.com>