one gets elliptic functions if one try direct method, The trouble with approximations is that it is hard to tell if they converge.....
>From your post I could not figure out, what is your question. May be you should formulate it clearer, so that we see, if somebody might help. There is a second problem: the code above does not look like Mathematica syntax, and I really cannot understand, what it means. I propose that you rewrite it in a legal Mathematica way, and, if after that it still does not work, send it once more.
Have fun, Alexei Alexei BOULBITCH, Dr., habil. IEE S.A. ZAE Weiergewan, 11, rue Edmond Reuter, L-5326 Contern, LUXEMBOURG