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Re:More Anomalous Behaviour with Indexed Variables
 Subject: [mg3307] Re:[mg3256] More Anomalous Behaviour with Indexed Variables
 From: fransm at win.tue.nl (Frans Martens)
 Date: 25 Feb 1996 14:42:02 0600
 Approved: usenet@wri.com
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 Newsgroups: wri.mathgroup
 Organization: Wolfram Research, Inc.
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Begin forwarded message:
>From: Mark James <mrj at cs.usyd.edu.au>
>To: mathgroup at smc.vnet.net
>Organization: The University of Sydney
>Subject: [mg3256] More Anomalous Behaviour with Indexed Variables
A recent article on this group discussed the frequent failure
of FindRoot when the search variable is indexed (e.g. x[1]).
I have been having similar problems.
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} ]
=====
FURTHER EXPLANATION:
The second differential equation in the first NDSolve call
above depends of a parameter f that is a function of p.
This parameter is calculated as a side effect
of integrating the first differential equation.
(My actual equation set, is 1000 times more complicated than this,
and I really want to use the side effect method to efficiently
calculate a number of parameters each integration step that
would otherwise each be calculated many times per step.)
I have used this method for a year without problems.
But changing the parameter to f[1] does not work.
(I now need to use indexed parameters in my real system.
I have managed to get this real system to work if I substitute
every indexed variable by a nonindexed one: e.g. s[1] > s1 .)
Am I doing anything wrong, or is it a bug? If it is a bug:
Is there a workaround? Will it be fixed in 3.0?
Is this related to similar problems with indexed
variables in FindRoot?
Thanks for your help.
Mark James  EMAIL :
mrj at cs.usyd.edu.au 
Basser Department of Computer Science, F09  PHONE : +6123513423

The University of Sydney NSW 2006 AUSTRALIA  FAX : +6123513838

8888888888888888888888888888888*8888888888888888888888888888888888888
The second instruction with NDSolve did not work properly because the
expression f[1] in the equations is replaced by f[1.].
Solution are:
(* SOLUTION 1, PARAMETER IS f[1] *)
Clear[ f ];
f[a_Real] := f[Round[a]];
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} ]
(* SOLUTION 2, 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} ]
Surprisingly, the idea to give the attribute NProtectedAll to the
variable f does not work.
Frans Martens
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