BibTeX
@ARTICLE{
Corliss1982SOD,
AUTHOR = "George F. Corliss and Y. F. Chang",
TITLE = "Solving Ordinary Differential Equations Using {T}aylor Series",
JOURNAL = "{ACM} Transactions on Mathematical Software",
VOLUME = "8",
NUMBER = "2",
YEAR = "1982",
PAGES = "114144",
REFERRED = "MR 83g 65072; [Aberth1988PNA]; [Chang1986TAT]; [Corliss1988AoD]; [Gupt85a].",
KEYWORDS = "point algorithm; Taylor series; radius of convergence; preprocessing; automatic
differentiation.",
ABSTRACT = "A Fortran preprocessor program uses automatic differentiation to write a Fortran
object program which is then run to solve the system. Parts: \begin{enumerate} \item
Expand the series using recurrence relations. \item Estimate the radius of convergence of each
component. \item Select a step size by comparGUM1995Gttn with series for model problems.
\item Extend the solution by analytic continuation.\end{enumerate} The series analysis
provides valuable information about analytic properties of the solution like the location and order
of primary singularities. Taylor series methods are shown to be competitive with DVERK and DGEAR in
terms of speed and accuracy.",
ad_theotech = "Taylor Arithmetic"
}
