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Re: Another basic (?) question about RecurrenceTable and replacement

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  • Subject: [mg122415] Re: Another basic (?) question about RecurrenceTable and replacement
  • From: Dana DeLouis <dana01 at me.com>
  • Date: Fri, 28 Oct 2011 05:33:00 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

... using RecurrenceTable and computing sol[n/10,x[n],y[n]] only once ? 

Hi.  I don't have a solution, but perhaps a few ideas.
My guess is that using RecurrenceTable and FindRoot might not work well together.  My thinking
is that a Recurrence table uses more exact values, whereas FindRoot returns values at machine precision.

> I kind of got confused with my notations : I want to solve 
> x_0 = -2, y_0 = 0 

As a suggestion,  perhaps refer to the RSolve function.
That function uses a specific way to refer to previous values.
As a simple example, here are begging x & y values, and recurrence functions:

equ={
x[0]==0,
x[1]==1,
x[n]==x[n-2]+x[n-1],

y[0]==1,
y[n]==n*y[n-1]
};

Rsolve suggest a function for both x & y as a function of n.

RSolve[equ, {x[n],y[n]}, n]  //FullSimplify

{
x[n]->Fibonacci[n],
y[n]->Pochhammer[1,n]
}


Perhaps one of a few suggestions for your example might be to use your FindRoot function and generate a list of x & y pairs.
Round to something more exact if your can.
For example, suppose FindRoot gave the following x & y pairs :

z={{1, 2.00001},{2, 4.9999999},{3, 10.00000001},{4, 19},{5, 36},{6, 69},{7, 134}};

If it is acceptable, try to round the values to something like this:

z={{1,2},{2,5},{3,10},{4,19},{5,36},{6,69},{7,134}};

I don't see a pattern, but FindSequenceFunction did.

FindSequenceFunction[z,n]

-1+2^n+n


I hope I understood your question correctly.
= = = = = = = = = = = = = = = = = = = = = = 
HTH
Dana DeLouis
$Version
8.0 for Mac OS X x86 (64-bit) (February 23, 2011)




On Oct 25, 6:19 am, victorphy <vba... at gmail.com> wrote:
> Hello,
> 
> here is another question I could'nt find the asnwer on the web,
> altough I guess it's very elementary.
> 
> Here is my problem. Assume I want to solve an implicit equation on two
> variables :
> 
> x_0 = _2, y_0 = 0
> 
> (x_{n+1},y_{n+1}) = sol(n/10,x_n,y_n)
> for n = 1..10
> 
> where f cannot be defined explicitely but is given by something like
> (I give  a silly exemple):
> 
> f[x_, a_] := -(x - a)^3 + (x - a)
> sol[a_?NumericQ, b_?NumericQ,c_?NumericQ] := FindRoot[{f[x, a], x +
> y}, {x, b}, {y, c}]
> 
> What is the way to write this using RecurrenceTable and computing
> sol[n/10,x[n],y[n]] only once ? (as in the real life the rootsearching
> is longer than above) ?
> 
> Any help would be very welcome.
> 
> Thank you very much in advance.
> 
> Best regards,
> 
> Victor





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