Iterate initial conditions

• To: mathgroup at smc.vnet.net
• Subject: [mg48775] Iterate initial conditions
• From: "Michael Hohendorf" <se0085 at uni-essen.de>
• Date: Wed, 16 Jun 2004 04:54:27 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

I have a system of differential equations, wich are results in two
functions f[x], g[x].
Now I have to iterate the initial conditons
(Tau_11[0],Tau_22[0],Tau_33[0]) until the functions f[x] and g[x] are
equal to other functions Sigma_m[x] and Sigma_u[x].
Can someone help me to solve my problem?

Michael

solution = NDSolve[{
Tau_11'[x] == (2 a_T[x] v'[x] Î·[x] - Exp[Epsilon[x] Î»[x](Ï?au_11[x]
+ Tau_22[x] + Tau_33[x])/Î·[x]] Ï?au_11[x] + 2 a_T[x] v'[x] Î·[x] Î»[x] (1 -
Î¾)) 1/(a_T[x]v[x]Î»[x]),

Tau_22'[x] == (2 a_T[x] Î·[x] (v[x] s'[x]/s[x])- Exp[Epsilon[x]
Î»[x](Ï?au_11[x] + Tau_22[x] + Tau_33[x])/Î·[x]] Ï?au_22[x] + 2 a_T[x] Î·[x]
Î»[x] (v[x] s'[x]/s[x]) (1 - Î¾)) 1/(a_T[x]v[x]Î»[x]),

Tau_33'[x] == (2 a_T[x] Î·[x] (v[x] r'[x]/r[x])- Exp[Epsilon[x]
Î»[x](Ï?au_11[x] + Tau_22[x] + Tau_33[x])/Î·[x]] Ï?au_33[x] + 2 a_T[x] Î·[x]
Î»[x] (v[x] r'[x]/r[x])(1 - Î¾)) 1/(a_T[x]v[x]Î»[x]),

Tau_12'[x] == (a_T[x] Î»[x] v'[x] r'[x] Tau_12[x] (1 - Î¾) + a_T[x] Î»[x]
Tau_12[x] (v[x] s'[x]/s[x]) (1 - Î¾) - Exp[Epsilon[x] Î»[x](Ï?au_11[x]
+ Tau_22[x] + Tau_33[x])/Î·[x]] Ï?au_12[x]) 1/(a_T[x]v[x]Î»[x]),

Tau_11[0]==a , Tau_22[0]==b , Tau_33[0]==c , Tau_12[0]==9810},
{Tau_11[x],Tau_22[x],Tau_33[x],Tau_12[x]},{x,0,0.42}]

Tau_11[x_]=Tau_11[x]/.solution[[1]]
Tau_22[x_]=Tau_11[x]/.solution[[1]]
Tau_33[x_]=Tau_11[x]/.solution[[1]]
Tau_12[x_]=Tau_11[x]/.solution[[1]]

f[x_]=Tau_11[x]-Tau_22[x]
g[x_]=Tau_22[x]-Tau_33[x]

Iterate initial conditions until

f[x]==Sigma_m[x]
g[x]==Sigma_u[x]

```

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