Re: Solving Ordinary differential equations by NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg104975] Re: [mg104962] Solving Ordinary differential equations by NDSolve*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sun, 15 Nov 2009 20:47:27 -0500 (EST)*Reply-to*: hanlonr at cox.net

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"?