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Question: How do I solve a non-linear integral equation? (numerically)

Question:How do I solve a non-linear integral equation? (numerically)

jbendler 20 Maple 18
integral
April 27 2015
2

Any suggestions (or perhaps related examples?) illustrating how I might numerically solve for f(t) in the following non-linear integral equation?  In Fortran, I would start with a guess f(t)=T0, and then search in the neighborhood for a minimum (in the error), but I am not familiar with numerical searches and methods in Maple.  Thank you for any suggestions or leads.

(a,b,... etc are all real)


> 

T__0 := 298.
> 

`ΔT` := 25.
> 

0 < beta and beta <= 1
> 

``
> 

f*t = T[0]+`&Delta;T`*[1-exp(-a(int(exp(-b/f(y)), y = y[1] .. t))^beta)]
> 

NULL


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