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Re: solving 8-dimensional ODE-System - error

• To: mathgroup at smc.vnet.net
• Subject: [mg123059] Re: solving 8-dimensional ODE-System - error
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Tue, 22 Nov 2011 05:34:17 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201111210925.EAA14641@smc.vnet.net>
• Reply-to: drmajorbob at yahoo.com

The error message says the function e appears with no arguments.

And that's true... in your definition of f, fk, cdot, ldot, edot, ndot,  
and B. So fix it.

You have functions that DO have arguments but don't depend on them, too.  
For instance,

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])))

-n (\[Rho] + (
    n (-1 - \[Eta] \[Phi] \[Psi] + \[Omega] + (
       e^Subscript[\[Alpha], 3] k^Subscript[\[Alpha], 1] (h l)^
        Subscript[\[Alpha],
        2] (1 - Subscript[\[Alpha],
          1] - \[Phi] \[Psi] Subscript[\[Alpha], 2] -
          Subscript[\[Alpha], 3]))/c))/v)

doesn't depend on Nu, S, k, l, or e. It does depend on n and c, but you've  
made it difficult to tell.

Because of this, your mention of ndot in "diffequ":

ndot[Nu[t], S[t], k[t], h[t], c[t], l[t], e[t], n[t]]

makes no sense. It looks as if t matters in several positions where it  
actually doesn't.

Bobby

On Mon, 21 Nov 2011 03:25:07 -0600, Xage <p.wirthumer at gmx.at> wrote:

> 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
>


-- 
DrMajorBob at yahoo.com

• References:
  • solving 8-dimensional ODE-System - error
    • From: Xage <p.wirthumer@gmx.at>