Solving recursively defined function - "not a valid limit of integration" error
- To: mathgroup at smc.vnet.net
- Subject: [mg123931] Solving recursively defined function - "not a valid limit of integration" error
- From: micha_cologne <michael.zaehringer at googlemail.com>
- Date: Sat, 31 Dec 2011 01:59:59 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
I am looking for the solution of a real-valued function f1[x] which is
defined recursively (f1[x] is contained in the functions g1[] and h1[]
below).
First I tried to use "Reduce" but it didn't work (Reduce::nsmet: This
system cannot be solved with the methods available to Reduce. >>). For
a less complex problem of this kind it worked though.
When I try to solve for the function f1[x] using "N[Solve[]]" I get
the error message "NIntegrate::nlim: y = x is not a valid limit of
integration. >>", see below:
-------------------------------------
In[213]:= g1[y_, z_] := (13/15 *y + (z - y)*(f1[y] - 2/15)) / (1 -
15/13 (1 - y) (1 - f1[y]));
In[214]:= h1[y_, z_] := (f1[y] - 2/15) / (1 - 15/13 (1 - y) (1 -
f1[y]));
In[215]:= sol = N[Solve[ { f1[0] == 2/15,
f1[x] ==
2/15 + (221/(4 + 221 (1 - 15/13 (1 - f1[x]) (1 - x))^2))*
Integrate[
y + 2*Integrate[
z (1 - g1[y, z]) - z^2 h1[y, z] - z^2 (1 - g1[y, z])^2 +
z^3 (1 - g1[y, z] h1[y, z]), {z, y, 1} ], {y, 0, x}]},
f1[x]]]
During evaluation of In[215]:= NIntegrate::nlim: y = x is not a valid
limit of integration. >>
During evaluation of In[215]:= General::stop: Further output of
NIntegrate::nlim will be suppressed \
during this calculation. >>
-------------------------------------------
Any suggestions how I can solve this problem? Your help is much
appreciated!
Happy New Year!
Michael