Publication: Solving Ordinary Differential Equations Using Taylor Series
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Solving Ordinary Differential Equations Using Taylor Series

- Article in a journal -
 

Author(s)
George F. Corliss , Y. F. Chang

Published in
ACM Transactions on Mathematical Software

Year
1982

Abstract
A Fortran pre-processor program uses automatic differentiation to write a Fortran object program which is then run to solve the system. Parts:

  1. Expand the series using recurrence relations.
  2. Estimate the radius of convergence of each component.
  3. Select a step size by comparGUM1995Gttn with series for model problems.
  4. Extend the solution by analytic continuation
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 Theory and Techniques
Taylor Arithmetic

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 = "114--144",
       REFERRED = "MR 83g 65072; [Aberth1988PNA]; [Chang1986TAT]; [Corliss1988AoD]; [Gupt85a].",
       KEYWORDS = "point algorithm; Taylor series; radius of convergence; pre-processing; automatic
         differentiation.",
       ABSTRACT = "A Fortran pre-processor 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"
}


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