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Michael Hohendorf
06/08/04 09:18am

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],Tau_12[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] η[x] - Exp[Epsilon[x] λ[x](τau_11[x] + Tau_22[x] + Tau_33[x])/η[x]] τau_11[x] + 2 a_T[x] v'[x] η[x] λ[x] (1 - ξ)) 1/(a_T[x]v[x]λ[x]),

Tau_22'[x] == (2 a_T[x] η[x] (v[x] s'[x]/s[x])- Exp[Epsilon[x] λ[x](τau_11[x] + Tau_22[x] + Tau_33[x])/η[x]] τau_22[x] + 2 a_T[x] η[x] λ[x] (v[x] s'[x]/s[x]) (1 - ξ)) 1/(a_T[x]v[x]λ[x]),

Tau_33'[x] == (2 a_T[x] η[x] (v[x] r'[x]/r[x])- Exp[Epsilon[x] λ[x](τau_11[x] + Tau_22[x] + Tau_33[x])/η[x]] τau_33[x] + 2 a_T[x] η[x] λ[x] (v[x] r'[x]/r[x])(1 - ξ)) 1/(a_T[x]v[x]λ[x]),

Tau_12'[x] == (a_T[x] λ[x] v'[x] r'[x] Tau_12[x] (1 - ξ) + a_T[x] λ[x] Tau_12[x] (v[x] s'[x]/s[x]) (1 - ξ) - Exp[Epsilon[x] λ[x](τau_11[x] + Tau_22[x] + Tau_33[x])/η[x]] τau_12[x]) 1/(a_T[x]v[x]λ[x]),

Tau_11[0]==a , Tau_22[0]==b , Tau_33[0]==c , Tau_12[0]==d},
{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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Subject (listing for 'Iterate initial conditions')
Author Date Posted
Iterate initial conditions Michael Hohe... 06/08/04 09:18am
Re: Iterate initial conditions Henry Lamb 06/17/04 01:53am
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