I knew Dr Chang. I also ran across that other paper several years ago,
though it would be good to give it another look. My work on this is at
http://sode.sourceforge.net/ Last Wednesday, I found an error in Dr
Corliss' three term analysis to estimate the radius of convergence and
order of singularities. I wrote Dr. Corliss then, but have not heard
back. Dr Chang used that formula and also is also used it in his six
term analysis. I also know Dr Corliss - but have not seen him for over
35 years. I have the BYTE article and a much more recent version of
Dr. Chang's program. I used Dr Chang's typescript (I believe it was
never finished) in my work - a link to a scan of it is on my web page.
I did not use his program - it is in FORTRAN and hard to follow. I
could not get the analysis of poles (especially the order) to work
right - and then discovered the error. There is more on that in the
notes on that web page. My program to solve odes is in Ruby, but
generates code for maxima, Maple, c, c++ or Ruby.
Dennis Darland
Quoting Barton Willis <willisb at unk.edu>:
> Thanks for the reference--it allowed me to recall a BYTE article on
> Taylor methods for ODEs. Sometime ago there was a
> thread about Taylor methods--I wasn't able to come up with the reference:
>
> @ARTICLE{
> Chang1986TAT,
> AUTHOR = "Chang, Y. F.",
> TITLE = "The {ATOMCC} Toolbox",
> JOURNAL = "BYTE",
> VOLUME = "11",
> NUMBER = "4",
> YEAR = "1986",
> PAGES = "215--224",
> REFERRED = "[Corliss1988AoD].",
> KEYWORDS = "point algorithm; Taylor series; automatic
> differentiation.",
> ABSTRACT = "ATOMCC is a pre-processor which accepts a
> Fortran-like statement of a system of
> ordinary differential equations and writes a Fortran object
> program which is run later to solve the
> system. The object program uses recurrence relations to
> generate the series and a radius of
> convergence analysis to choose a stepsize which controls
> the local error. The program also solves
> stiff systems. It runs on IBM PC compatible computers up to
> large mainframes."}
>
> --Barton
>
> ________________________________________
>
> I came across this paper (dedicated to memory of Wm Schelter!)
>
> http://www.maia.ub.es/~angel/taylor/taylor.pdf
>
>
>
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