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One method of solving Fredholm equations. Say you have a Fredholm integral equation of the second kind:

               a
f(x) = g(x) + ∫ K(x,t) f(t) dt
               b

To solve it, we take the limit of

         n   i
f (x) =  ∑  λ u (x)
 n      i=0    i

as n approaches ∞, where ui(x) is:

u (x) = g(x)
 0
         b
u (x) = ∫  K(x,t )g(t ) dt
 1       a      1    1    1
         b  b
u (x) = ∫  ∫  K(x,t )K(t , t ) g(t ) dt dt
 2       a  a      1    1   2     2    2  1
         b b     b
u (x) = ∫ &int ... ∫  K(x,t )K(t , t ) ...
 n       a a     a      1    1   2
               K(t   ,t ) g(t ) dt dt   ... dt
                  n-1  n     n    n  n-1      1

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