I would not fret if it converges slowly.

For example, the slog solution with (E-I)*f=1 converges very slowly, with terms being inaccurate by 10% or more after perhaps the first 1/4th or 1/3rd of the series.

For example, for the 200x200 solution, only the first 75 or so terms are accurate to within 20%, only 60 or so to within 10%. And only the first 35 or so terms are accurate to within 1%. The first 20 or so are accurate to within 0.1%.

And after about the 90th or 100th term, it's essentially garbage. The purposes of those 110 garbage terms is to make sure that the first 90 non-quite-garbage terms still give us a decent solution.

For a 400x400 system, those numbers roughly double (a little less in fact), giving roughly 65-70 terms to within 1%, and about 100 terms to within 10%. For a 600x600 system, we reach 1% inaccuracies already by the 80th term, and 10% by about 140 terms.

Since the singularities for the slog are logarithmic to first approximation, I'd expect a similar result for the natural logarithm.

For example, the slog solution with (E-I)*f=1 converges very slowly, with terms being inaccurate by 10% or more after perhaps the first 1/4th or 1/3rd of the series.

For example, for the 200x200 solution, only the first 75 or so terms are accurate to within 20%, only 60 or so to within 10%. And only the first 35 or so terms are accurate to within 1%. The first 20 or so are accurate to within 0.1%.

And after about the 90th or 100th term, it's essentially garbage. The purposes of those 110 garbage terms is to make sure that the first 90 non-quite-garbage terms still give us a decent solution.

For a 400x400 system, those numbers roughly double (a little less in fact), giving roughly 65-70 terms to within 1%, and about 100 terms to within 10%. For a 600x600 system, we reach 1% inaccuracies already by the 80th term, and 10% by about 140 terms.

Since the singularities for the slog are logarithmic to first approximation, I'd expect a similar result for the natural logarithm.

~ Jay Daniel Fox