let be the integral equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] f(x)=\lambda \int_{0}^{1}dyK(x,y)f(y) [/tex]

where the Kernel is known and "lambada" is an small eigenvalue... the question is if i want to solve i propose the iterative scheme:

[tex] f_{n+1} (x)=\lambda \int_{0}^{1}dyK(x,y)f_n(y) [/tex]

My question is if in this case i can propose a "Neumann series" for the resolvent Kernel R(x,y) in the form...

[tex] R= \sum_{n=0}^{\infty} \lambda ^ n K^{n} [/tex]

for K^n the n-th iterated kernel since the equation is HOmogeneus (all the functions involved except the Kernel are unknown) or if we have enough with the iteration procedure to solve the equation..thanks.

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# Iterative methods

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