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Re: Wrapping NDSolve within a function

• To: mathgroup at smc.vnet.net
• Subject: [mg126344] Re: Wrapping NDSolve within a function
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Thu, 3 May 2012 04:34:56 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201205020944.FAA19622@smc.vnet.net>

predState[rg_, rp_, rh_, Mg_, Mp_, Mh_] :=
 Module[
  {parmListND3woC, A, B, Rb, Rc, g, p, q},
  parmListND3woC =
   {A -> Mg/rg, B -> Mp/rg, C -> Mh/rg,
    Rb -> rp/rg, Rc -> rh/rg};
  {g, p, q} /. NDSolve[{
       g'[t] == g[t]*(1 - g[t] - p[t] - q[t]) -
         A*g[t]*g[t],
       p'[t] == Rb*p[t]*(1 - p[t] - q[t]) -
         B*p[t]*g[t],
       q'[t] == Rc*q[t]*(1 - q[t]) -
         C*q[t]*g[t],
       g[0] == 0.5,
       p[0] == 0.5,
       q[0] == 0.5} /.
      parmListND3woC,
     {g, p, q}, {t, 0, 1000}][[1]]]

{g, p, q} =
  predState[1.5, 0.4, 0.2, 0.1, 0.0002, 0.0099];

Plot[{
  Tooltip[g[t], "g[t]"],
  Tooltip[p[t], "p[t]"],
  Tooltip[q[t], "q[t]"]},
 {t, 0, 100}]


Bob Hanlon


On Wed, May 2, 2012 at 5:44 AM, bbeckage <Brian.Beckage at uvm.edu> wrote:
> When I try to return the interpolating function produced by NDSolve from
> within a function, the object returned has an unexpected $7360 appended,
> e.g.,
>
> out = predState[1.5, 0.4, 0.2, 0.1, 0.0002, 0.0099]
>
> (where predState is defined further below) results in
>
> =
> {{g$7360->InterpolatingFunction[{{0.,1000.}},<>],p$7360->InterpolatingFunction[{{0.,1000.}},<>],q$7360->InterpolatingFunction[{{0.,1000.}},<>]}}
>
> Note the g$7360 rather than just g.  If NDSolve is not wrapped within
> the function, it returns a plain 'g', i.e., g->InterpolatingFunction....
>  The appended $7360 makes it difficult to use the interpolating function
> as I can't reference it within other functions as the integer changes
> with each function call, e.g., g$7360[10] /. out, then g$7370[10] /.
> out, rather than being able to access it using the expected g[10]/.out.
>
> Why  is this $7360 appended to g?  How can NDSolve be wrapped in a
> function, but be made to return a plain g?
>
> Thanks for your help.
>
> Best wishes,
> Brian
>
>
>
> predState[rg_, rp_, rh_, Mg_, Mp_, Mh_] :=
>  Module[{parmList3woC, parmListND3woC, A, B, Rb, Rc, g, p, q, solND},
>  parmListND3woC = {A -> Mg/rg, B -> Mp/rg, C -> Mh/rg, Rb -> rp/rg,
>    Rc -> rh/rg};
>  solND =
>   NDSolve[{
>     g'[t] == g[t]*(1 - g[t] - p[t] - q[t]) - A*g[t]*g[t] /. parmListND3woC,
>     p'[t] == Rb*p[t]*(1 - p[t] - q[t]) - B*p[t]*g[t] /. parmListND3woC,
>     q'[t] == Rc*q[t]*(1 - q[t]) - C*q[t]*g[t] /. parmListND3woC, g[0] == 0.5,
>      p[0] == 0.5, q[0] == 0.5}, {g, p, q}, {t, 0, 1000}];
>  Return[solND]
>  ]

• References:
  • Wrapping NDSolve within a function
    • From: bbeckage <Brian.Beckage@uvm.edu>