I am attempting to write a program that will be able to numerically solve a homogeneous Fredholm Integral Equation of Second Kind, with a Symmetric Kernel. I have been looking through textbooks and websites for some time, but most of literature are concerned with the derivation for continuous functions. Since the program will have to be discrete, I was wondering if anybody knew of any ways to solve this integral equation discretely. My plan was to be able to generate an arbitrary symmetric Kernel and let the program solve for the eigenvalues and eigenfunctions. If anybody can help me out with this, and hopefully provide me with a reference it would be greatly appreciated.
Thank you very much.