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MathGroup Archive 2005

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Re: function of a function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62693] Re: function of a function
  • From: "Narasimham" <mathma18 at hotmail.com>
  • Date: Wed, 30 Nov 2005 22:09:18 -0500 (EST)
  • References: <dmjvuc$77e$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Yes, absolutely.. Thanks to you and Jens.  :)  Actually I was
temporarily swayed by so many postings in the thread and accepted the
implicit suggestion that the problem is well posed !  [ To solve  an
ODE F ( f (x), y, y' ) = 0 is  OK, but not F (  f (x), f (y), y'  ) ! ]


Regards
Narasimham

Andrzej Kozlowski wrote:
> On 30 Nov 2005, at 14:07, Narasimham wrote:
>
> > Jens-Peer Kuska wrote:
> >
> >> it can't work because f [0] ==1 given in your differential equation
> >> f ' [0]==f [1] and NDSolve[] can't find the value for
> >> f[1] until it has integrated the equation.
> >
> > ???
> >
> >> The nested dependence is equivalent to an infinite
> >> system of ordinary differential equations and it seems to be
> >> hard to do this by a finte computer.
> >
> > I cannot understand this. In the following two examples the first one
> > works, not the second.
> >
> > Clear[x,f,EQ];
> > EQ={f'[x] == f[Cos[x]],f[0]== 1};
> > NDSolve[EQ,f,{x,0,4}];
> > f[x_]=f[x]/.First[%];
> > Plot[f[x],{x,0,4}];
> >
> > Clear[x,f,EQ];
> > EQ={f'[x] == Cos[f[x]],f[0]== 1};
> > NDSolve[EQ,f,{x,0,4}];
> > f[x_]=f[x]/.First[%];
> > Plot[f[x],{x,0,4}];
>
>
> Surely, you mean the second one works, the first one does not!? Also,
> I think I agree with Jens. These cases are quite different and the
> problem he mentione does not arise in the second case. Ine the second
> case the derivative at a point x is defined only in terms of the
> value of the function at x. Thus values of the function, it's
> derivative, function etc, can be computed sequentially. In the first
> case, however, in order to compute the derivative at x you need to
> know the value of the function at Cos[x], which in general will not
> be known yet. This is, I think, what Jens meant and it seems to me
> clearly right.
>
> >
> > It appears (to me) the power of programming with functions in
> > Mathematica has not been used to the full.
> >
> >
>
> What do you mean? Can you suggest an approximation scheme for this
> sort of problem?
>
> Andrzej Kozlowski
>
>
>
> > Jens-Peer Kuska wrote:
> >> Hi,
> >>
> >> it can't work because f[0]==1 give in your
> >> differential equation
> >> f'[0]==f[1] and NDSolve[] can't find the value for
> >> f[1] until it
> >> has integrated the equation.
> >> The neted dependence is equvalent to a infinite
> >> system of
> >> ordinary differential equations and it seems to be
> >> hard to do
> >> this by a finte computer.
> >>
> >> Regards
> >>   Jens
> >>
> >> "Narasimham" <mathma18 at hotmail.com> schrieb im
> >> Newsbeitrag news:dmha20$932$1 at smc.vnet.net...
> >> | Tried to solve numerically:
> >> |
> >> |
> >> http://groups.google.com/group/sci.math/browse_frm/thread/
> >> 248f76d024c1ac57/0bba983777a07bc9#0bba983777a07bc9
> >> |
> >> | thus:
> >> |
> >> | EQ= { f'[x] == f[f[x]], f[0]== 1} ;
> >> NDSolve[EQ,f,{x,0,2}];
> >> |
> >> | But gives an error.  NDSolve::ndnum:
> >> Differential equation does not
> >> | evaluate to a number at x = 0.
> >> |
> >> | Also does not work even with other f[0] values.
> >> Any way to do that?
> >> |
> >


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