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I have asked this question at MSE but got no response. I have rephrased it so that anyone who knows operator theory and integral equations could help me out... I faced a problem in physics which is a non-linear Fredholm integral equation (Hammerstein). It is of the form: \begin{equation} y(p)=f(p)+\int_0 ^{\infty}\frac{e^{ik∧p}}{y(k)}dk \end{equation} There are two subtleties:

  1. The kernel is non-degenerate or non-separable.
  2. The non-linearity is reciprocal.

The kernel is symmetric as the wedge product is anti-symmetric,i.e. $\overline{K(p,k)}=K(k,p)$. I tried solving it using the collocation method but got divergence due to it's severe bound on the upper limit. I am now starting to work with Monte-Carlo integration and it's too complicated. That's why I want to know if any of you could help me.

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  • $\begingroup$ Where did you ask this question previously? It would be nice to provide a link to avoid duplication of efforts. $\endgroup$ Feb 19, 2015 at 4:10
  • $\begingroup$ i asked it in math.stackexchange... $\endgroup$
    – arsal
    Feb 19, 2015 at 4:54
  • $\begingroup$ I added a link to your question and made minor other edits. Feel free to re-edit if you want to. $\endgroup$ Feb 19, 2015 at 5:06

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