Re: Solving Ordinary differential equations by NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg104976] Re: [mg104962] Solving Ordinary differential equations by NDSolve*From*: "David Park" <djmpark at comcast.net>*Date*: Sun, 15 Nov 2009 20:47:38 -0500 (EST)*References*: <27585103.1258283977493.JavaMail.root@n11>

One possible solution is to construct a second FunctionInterpolation, taking only the Re part, since the imaginary part is just round off errors. Also use Set instead of SetDelayed when calculating v[t]. 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_] = FunctionInterpolation[Re[V[t]] /. sol[[1]], {t, 0, 9}][t] Plot[v[t]*1000, {t, 0, 9}, PlotRange -> All] Grid[ Table[{t, v[t]}, {t, 0, 9, 1}]] David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Allamarein [mailto:matteo.diplomacy at gmail.com] 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"?