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MathGroup Archive 1996

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Re: More Anomalous Behaviour with Indexed Variables

  • To: mathgroup at smc.vnet.net
  • Subject: [mg3306] Re: [mg3256] More Anomalous Behaviour with Indexed Variables
  • From: jpk at apex.mpe.FTA-Berlin.de (Jens-Peer Kuska)
  • Date: Sun, 25 Feb 1996 03:20:17 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

> Now this has cropped up again with NDSolve.  If you
> get a chance, run the following two groups of expressions
> through your version.  Why does the second version fail?
> Is it because NDSolve no longer evaluates the dummy equation
> first? I am using 2.2.1.
> 
> (*
>     PARAMETER IS: f
> *)
>     Clear[ f ];
>     calc[ v_Real ] := ( f = v^2; 0 );
>     NDSolve[ {dummy'[t] == calc[p[t]], dummy[0]==0,
>               p'[t] == -p[t] + f, p[0]==0 }, {dummy,p}, {t,0,1} ]
> 
> (*
>     PARAMETER IS: f[1]
> *)
>     Clear[ f ];
>     calc[ v_Real ] := ( f[1] = v^2; 0 );
>     NDSolve[ {dummy'[t] == calc[p[t]], dummy[0]==0,
>               p'[t] == -p[t] + f[1], p[0]==0 }, {dummy,p}, {t,0,1} ]
> 
> Thanks for your help.
> 
> Mark James                

Hi Mark,

at first 
  I think that it is really dangerous to use sutch side 
  effect, because there is *no* guarantie that NDSolve evaluate
  the differential equations in the same order as given. NDSolve
  has to do a lot of things bevore it can start with the numerical
  solution. 

at second
  don't talk about efficient solutions, Mathematica is a interpreter
  and will be allways 100 or more times slower than a compiled
  code. You can still using Mathematica via MathLink for dawing and post processing.

You mix up in Your code assignet function values and indexing. f[1]=v^2 will assign
the value v^2 to the function f[z] for z=1, indexing f[[1]]=v^2 mean that the first component
of the vector f has the value v^2. How ever here is a working example

(*
    PARAMETER IS: f[[1]]
*)
    Clear[ f,calc ];
    f={0.};
    calc[ v_Real ] := ( f[[1]] = v^2; 0 )
    NDSolve[ {dummy'[t] ==calc[p[t]], dummy[0]==0,
              p'[t] == -p[t] + f[[1]], p[0]==0 }, 
              {dummy,p}, {t,0,1},Compiled->False ]


{{dummy -> InterpolatingFunction[{0., 1.}, <>], 
 
   p -> InterpolatingFunction[{0., 1.}, <>]}}

Hope that helps
Jens



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