11/22/2013, 11:20 PM

Interesting. It'd be nice to see if these results could be reproduced with the Kouznetsov/HAM technique, but I'm still playing with it. One of the things (which I should mention when I post more details in that thread) is that the HAM requires the choice of an "auxiliary linear operator", and the choice of that auxiliary linear operator is determined by the form in which we express the solution of the integral equation to be solved (in this case the Kouznetsov Cauchy equation). I was able to get some convergence for other bases using a linear operator given by the identity, but convergence was not very good, taking a fair number of iterations just to get a single digit of convergence. It would be interesting to see if there are methods to speed the covergence. From what I've read, the choice of linear operator is important and can affect the speed of covergence, and I'm not sure on what the right "form to express the solution" (the "rule of solution expression") is. I'll post about this on the HAM thread.