Re: function of a function

*To*: mathgroup at smc.vnet.net*Subject*: [mg62650] Re: function of a function*From*: "Narasimham" <mathma18 at hotmail.com>*Date*: Wed, 30 Nov 2005 00:07:02 -0500 (EST)*References*: <dmha20$932$1@smc.vnet.net><dmhfhd$bit$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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}]; It appears (to me) the power of programming with functions in Mathematica has not been used to the full. Regards Narasimham 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? > |