Re: NDSolve can't solve a complex ODE correctly?

*To*: mathgroup at smc.vnet.net*Subject*: [mg74923] Re: NDSolve can't solve a complex ODE correctly?*From*: m.r at inbox.ru*Date*: Wed, 11 Apr 2007 02:00:40 -0400 (EDT)*References*: <evd3uh$5ks$1@smc.vnet.net>

Barrow wrote: > Dear all, > I have two coupled ordinary differential equations which satisfied > by two functions, a(t) and az(t). It can be shown analitically that as > t approaches infinity, a(t) approaches az(t). But the numerical > solution given by Mathematica doesn't agree this. > Here is my code: > ----------------------- > lam = 1; > eqb = ((a'[t]/a[t])^2 + 2a'[t]*az'[t]/a[t]/az[t] == lam); > eqaz = (3(a'[t]/a[t])^2 + 2(a''[t]/a[t] - (a'[t]/a[t])^2) == lam); > sol = NDSolve[{eqb, eqaz, a[0] == 1, az[0] == .5, a'[0] == .6}, {a[t], > az[t]}, {t, 0, 2000}, MaxSteps -> 20000]; > Plot[Evaluate[{a[t]/az[t]} /. sol], {t, 0, 2000}, PlotStyle -> > {Hue[1]}]; > ---------------------------------- > The result of the plot is an oscillation around 2.07846 which is > really strange. > Is there anything I didn't noticed about NDSolve or any method to > improve my coding? > Thanks very much! > Cheers. Barrow You can solve your equations exactly if you do it step by step: sola = First@ DSolve[eqaz, a, t] solapar = First@ Solve[{a[0] == 1, a'[0] == 6/10} /. sola] solaz = First@ DSolve[eqb /. sola, az, t, GeneratedParameters -> C2] solazpar = First@ Solve[az[0] == 5/10 /. solaz /. solapar] Limit[a[t]/az[t] /. solaz /. solazpar /. sola /. solapar, t -> Infinity] // TrigToExp // FullSimplify Out[10]= (6*Sqrt[3])/5 Maxim Rytin m.r at inbox.ru