solving 8-dimensional ODE-System - error
- To: mathgroup at smc.vnet.net
- Subject: [mg123021] solving 8-dimensional ODE-System - error
- From: Xage <p.wirthumer at gmx.at>
- Date: Mon, 21 Nov 2011 04:25:07 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
Dear readers, I'm trying to analyse a big system in mathematica but when trying to use "NDSolve", i always get various errors. I tried many ways but no solution. Please help me on that. Here's my code: (*Definition der DE*) Q = Exp[-S] Q' = D[Q, S] Ndot[Nu_, S_, k_, h_, c_, l_, e_, n_] = (n - d)*Nu; Sdot[Nu_, S_, k_, h_, c_, l_, e_, n_] = Nu*e - \[Delta]*S; hdot[Nu_, S_, k_, h_, c_, l_, e_, n_] = \[Psi]*(1 - l - \[Phi]*n)*h; kdot [Nu_, S_, k_, h_, c_, l_, e_, n_] = f - c - (n - d)*k; f = k^Subscript[\[Alpha], 1] (l*h)^Subscript[\[Alpha], 2] e^ Subscript[\[Alpha], 3] ; fk = D[f, k]; cdot[Nu_, S_, k_, h_, c_, l_, e_, n_] = c*(fk - \[Rho] - (n - d)) ldot[Nu_, S_, k_, h_, c_, l_, e_, n_] = l*(-(1 - Subscript[\[Alpha], 3])*A - Subscript[\[Alpha], 3]*B + Subscript[\[Alpha], 1] kdot[Nu, S, k, h, c, l, e, n]/k + Subscript[\[Alpha], 2] hdot[Nu, S, k, h, c, l, e, n]/h - cdot[Nu, S, k, h, c, l, e, n]/c)/(1 - Subscript[\[Alpha], 2] - Subscript[\[Alpha], 3]); edot[Nu_, S_, k_, h_, c_, l_, e_, n_] = e*(-Subscript[\[Alpha], 2]*A - (1 - Subscript[\[Alpha], 2])*B + Subscript[\[Alpha], 1] kdot[Nu, S, k, h, c, l, e, n]/k + Subscript[\[Alpha], 2] hdot[Nu, S, k, h, c, l, e, n]/h - cdot[Nu, S, k, h, c, l, e, n]/c)/(1 - Subscript[\[Alpha], 2] - Subscript[\[Alpha], 3]) ; ndot[Nu_, S_, k_, h_, c_, l_, e_, n_] = - n*(\[Rho] + n/v (\[Omega] - \[Phi]*\[Psi]*\[Eta] - 1 + f/c (1 - Subscript[\[Alpha], 1] - \[Phi]*\[Psi]*Subscript[\[Alpha], 2] - Subscript[\[Alpha], 3]))); A = \[Rho] - \[Psi]*l - \[Psi]*\[Eta]*c*l/(Subscript[\[Alpha], 2]*f); B = \[Rho] + \[Delta] + (n - d) + \[Sigma]*Nu*e*Q'* c/(Subscript[\[Alpha], 3]*Q*f); (*Solve it!*) param = {\[Rho] -> 0.1, \[Delta] -> 0.1, d -> 0.04, Subscript[\[Alpha], 1] -> 0.3, Subscript[\[Alpha], 2] -> 0.3, Subscript[\[Alpha], 3] -> 0.05, \[Nu] -> 0.1, \[Omega] -> 0.1, \[Sigma] -> 0.1} diffequ[Nu0_, S0_, k0_, h0_, c0_, l0_, e0_, n0_] = {Nu'[t] == Ndot[Nu[t], S[t], k[t], h[t], c[t], l[t], e[t], n[t]], S'[t] == Sdot[Nu[t], S[t], k[t], h[t], c[t], l[t], e[t], n[t]], h'[t] == hdot[Nu[t], S[t], k[t], h[t], c[t], l[t], e[t], n[t]], k'[t] == kdot[Nu[t], S[t], k[t], h[t], c[t], l[t], e[t], n[t]], c'[t] == cdot[Nu[t], S[t], k[t], h[t], c[t], l[t], e[t], n[t]], l'[t] == ldot[Nu[t], S[t], k[t], h[t], c[t], l[t], e[t], n[t]], e'[t] == edot[Nu[t], S[t], k[t], h[t], c[t], l[t], e[t], n[t]], n'[t] == ndot[Nu[t], S[t], k[t], h[t], c[t], l[t], e[t], n[t]], Nu[0] == Nu0, S[0] == S0, k[0] == k0, h[0] == h0, c[0] == c0, l[0] == l0, e[0] == e0, n[0] == n0 } /. param // Together; var = {Nu[t], S[t], k[t], h[t], c[t], l[t], e[t], n[t]}; NDSolve[diffequ[.5, .5, .5, .5, .5, .5, .5, .5] /. param, var, {t, 0, 1}] I'm looking forward to a solution! Kind regards Peter
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