BibTeX
@INPROCEEDINGS{
         Halin1983Tao,
       AUTHOR = "Halin, Hans J.",
       TITLE = "The applicability of {T}aylor series methods in simulation",
       BOOKTITLE = "Proceedings of the 1983 Summer Computer Simultation Conference (Vancouver, B.C.)",
       VOLUME = "5",
       YEAR = "1983",
       KEYWORDS = "differentiation arithmetic; Taylor series; computer program; numerical results;
         convergence.",
       ABSTRACT = "The author surveys historical and current developements in the application of
         recurrent Taylor series to the integration of systems of ordinary differential equations. The
         historical developement of the subject is reviewed along with a discussion of the reasons for the
         existence of present day prejudice against the method. A summary of current techniques is presented
         including those for deriving the recurrence relations with particular emphasise towards
         implementation. Questions about convergence, stepsize control and automatic control of series length
         are considered. Various difficulties such as integration across discontinuities and implicit
         differential equations are discussed and accurate and efficient remedies are provided. A simulation
         language, PSCSP (Power Series Continuous-system Simulation Program), is presented. This is used as a
         medium for testing and comparing the theory discussed earlier."
}