Much more progress on differential equations

I have had 1st order equations working for a while, except when I broke things trying to fix other things. One thing I had trouble with was higher order equations. Now that is fixed. Also then there were higher order equations with derivatives on the right hand side. Now that is fixed also. Perhaps, I should digress. Although the program is designed to solve multiple ordinary differential equations, I am only working on single equations now. The highest order derivative is solved for (on the left hand side). The rest is on the right hand side. The program is written in Ruby and generates a Maple program. It is written to be able to also generate Maxima or Ruby. But I am only debugging Maple right now. After some more testing I expect to put it on SourceForge. Also I have also discovered that rounding error is overwhelming the truncation error, which should not have been such a big surprise. I have mostly been testing using Maple set to use 50 Digits and 30 Taylor series terms, but I am only getting about 16 digit accuracy. I remember at the University of Nerbraska, Lincoln when I was first introduced to the Long Taylor Series method by Professor Y. F. Chang, I estimated there would be a large round off error. This was 1977. Professor George Corliss thought the actual error would not actually be so large, or so I remember. Another Professor Lipsky thought the error would be a problem, or so, again, I remember. I have also been working on a Arbitrary Precision Floating Point library for Ruby, which tracks the maximum error possible using differentials. Although very slow, if it works, one could guarantee a certain accuracy. Also, I have such difficulty working things out that I sometimes doubt if I could pass freshman calculus again.