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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