Is the Neumann Series Always Effective for Solving Integral Equations?

[eljose]

Let be the integral equation:

$$\int_{a}^{b}dyK(x,y)f(y)=g(x)$$where f is unknown and g is known, then i use a resolvent Kernel in the form:

$$\int_{a}^{b}dyR(x,y)g(y)=f(x)$$ where we obtain the Kernel R by:

$$R=\sum_{n=0}^{\infty}b_{n}(K-I)^{n}$$ the last is Neumann series for the Kernel operator R..is my approach always true?..thanks.

 

[HallsofIvy]

Yes, that will work. It's a bit tedious in some cases.