I have used your latest worksheet to produce plots as shown below. I added a plot command for y(x). The plots all look what I expected qualitatively and semi-quantitatively.
See my worksheet below - plots don't show. I copy/pasted so that it led to changes in the text. I hope this is intelligible. If not I can change what is below to what actuallly appears in my file.
It is a shame that there is a problem with x<0.1.
Do you feel that my upcoming increase of RAM from 2Gb to 4Gb might help?
Also, I would like to produce three plots for y(x) and for L(x) using three values of e on one set of axes.
Is there a way to do this?
Finally, I want to express my gratitude to you for all your help and dedication to me and others.
> f := proc (x, y) options operator, arrow; -N+add(1/(exp(e*((n-x)^2-y))-1), n = -10 .. 10) end proc;
> fexpr := subs(N = 10000, e = 0.2e-1, d = 1/(e*N), f(x, Y));
> y := unapply(('fsolve')(fexpr, Y = 0 .. x^2), x);
> plot(proc (x) options operator, arrow; y(x) end proc, -.9 .. .9, color = black, thickness = 2);
> Lproto := proc (a, b) options operator, arrow; -add((n-a)/(exp(e*((n-a)^2-b))-1), n = -10 .. 10)/N end proc;
> L := subs(N = 10000, e = 0.2e-1, d = 1/(e*N), eval(Lproto));
> L(.452, y(.452));
> plot(proc (t) options operator, arrow; L(t, y(t)) end proc, .1 .. .49999, color = black, thickness = 2);