BibTeX
@INCOLLECTION{
         Corliss1984Ago,
       AUTHOR = "Corliss, George F. and Rall, Louis B.",
       TITLE = "Automatic generation of {T}aylor series in {P}ascal-{SC}: {B}asic operations and
         applications to differential equations",
       BOOKTITLE = "Trans. of the First Army Conference on Applied Mathematics and Computing
         (Washington, D.C., 1983)",
       PUBLISHER = "ARO Rep. 84-1, U. S. Army Res. Office",
       ADDRESS = "Research Triangle Park, N.C.",
       YEAR = "1984",
       PAGES = "177--209",
       REFERRED = "CMP 741 340; [Garl85a] \# 310; [Garl87a] \# 310; [Corliss1988AoD];
         [Fischer1987AD]; [Juedes1991ATo]; [Rall1987Oio].",
       COMMENT = "Also appeared as {\sl MRC Technical Summary Report No.2497,\/} Mathematics
         Research Center, University of Wisconsin-Madison, 1983.",
       KEYWORDS = "automatic differentiation; Taylor series; stability.",
       ABSTRACT = "Pascal-SC supports user-defined data types, user-defined operators, and accurate
         floating point and interval arithmetic for numerical computations. The authors implement data types
         TAYLOR and ITAYLOR (Interval Taylor) with operators $ + $, $ - $, $ * $, $ / $, $ ** $, and the
         functions SQR, SQRT, EXP, SIN, COS, ARCTAN, and LN. An initial value problem $ y' = y^2 $, $
         y(0) = 1 $, is solved with TAYLOR and with ITAYLOR types to show that the series generation exhibits
         a mild instability which has no significant effect on the values of the solution computed by
         analytic continuation."
}