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Topic: Recurrence Equation RSolve, no error shown, no solution?
Replies: 2   Last Post: Dec 17, 2012 2:54 AM

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 Dana DeLouis Posts: 24 Registered: 11/18/12
Re: Recurrence Equation RSolve, no error shown, no solution?
Posted: Dec 17, 2012 2:54 AM

> RSolve[{w[n + 1] == w[n] - 0.02/w[n], w[0] == 2}, w[n], n]
> Could someone tell me if there is possible to solve this and what's my error?

Hi. Just to add 2 cents on "what's my error"
Here, the next value of x is based on current value of x:

x - 1/(50 x)

We see that the values get smaller as we loop.
We also note that if the next value of x were zero, then we get a divide by zero error.

So, our values can only decrease until:

Solve[x-1/(50 x)==0]
{{x->-(1/(5 Sqrt[2]))},{x->1/(5 Sqrt[2])}}

%//N
{{x->-0.141421}, {x -> 0.141421}}

So, we can only decrease until our value reaches 1/(5 Sqrt[2]),
then we calculate zero for the next value, and encounter infinity, or div by 0.

Hense, I don't believe this is a True Recurrence Equation as one may have hoped.

Looks like the loop is only valid for about 102 loops. (At machine precision)

NestWhileList[#-1/(50 #)&, 2., # > 1/(5 Sqrt[2]) &] ;

% // Length
102

= = = = = = = = = =
HTH :>)
Dana DeLouis
Mac & Mathematica 8
= = = = = = = = = =

On Tuesday, December 11, 2012 7:54:32 PM UTC-5, Fran Alvarez wrote:
> Hi all!
>
> I'm looking for the solution of:
>
>
>
> RSolve[{w[n + 1] == w[n] - 0.02/w[n], w[0] == 2}, w[n], n]
>
>
>
> but the output is the same on the input and no error is shown. I've read the help that comes with Mathematica (I'm using 7.01 version for Mac) but no way. It seems to me that the main difference with the majority of examples shown in the help is the w[n] that appears as a denominator at the equation's RHS. I've seen complex rational examples at the help though, and RSolve manages to give a solution.
>
> Could someone tell me if there is possible to solve this and what's my error?
>
> Thank you!
>
> Fran =C1lvarez

Date Subject Author
12/13/12 Bob Hanlon
12/17/12 Dana DeLouis