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N[Solve[] leads to error "not a valid limit of integration"
Posted:
Dec 30, 2011 11:22 AM


I am looking for the solution of a realvalued 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



