Detail publikace

Methodology of the Taylor Series Based Computations

Originální název

Methodology of the Taylor Series Based Computations

Anglický název

Methodology of the Taylor Series Based Computations

Jazyk

en

Originální abstrakt

In this paper an outline is presented of historical and current developments in the application of recurrent Taylor series to the integration of systems of ordinary differential equations. The principal idea of an extremely accurate and fast method for numerical solutions of ordinary differential equations is presented in the paper. In general Taylor series are not included or not even mentioned in surveys on numerical integration techniques as the programs were written by mathematicians with the main objective of demonstrating the feasibility of the concept and with the goal of providing integration algorithms of very high accuracy. For this reason the programs should be looked upon as a stimulus for writing more advanced software employing Taylor series better able to compete with programs using other methods. An attempt in this direction is TKSL [8], a program the results of which will be dealt with.

Anglický abstrakt

In this paper an outline is presented of historical and current developments in the application of recurrent Taylor series to the integration of systems of ordinary differential equations. The principal idea of an extremely accurate and fast method for numerical solutions of ordinary differential equations is presented in the paper. In general Taylor series are not included or not even mentioned in surveys on numerical integration techniques as the programs were written by mathematicians with the main objective of demonstrating the feasibility of the concept and with the goal of providing integration algorithms of very high accuracy. For this reason the programs should be looked upon as a stimulus for writing more advanced software employing Taylor series better able to compete with programs using other methods. An attempt in this direction is TKSL [8], a program the results of which will be dealt with.

BibTex


@inproceedings{BUT30213,
  author="Martina {Drozdová} and Jan {Kopřiva} and Jiří {Kunovský} and Milan {Pindryč}",
  title="Methodology of the Taylor Series Based Computations",
  annote="In this paper an outline is presented of historical and current developments in
the application of recurrent Taylor series to the integration of systems of
ordinary differential equations. The principal idea of an extremely accurate and
fast method for numerical solutions of ordinary differential equations is
presented in the paper.
In general Taylor series are not included or not even mentioned in surveys on
numerical integration techniques as the programs were written by mathematicians
with the main objective of demonstrating the feasibility of the concept and with
the goal of providing integration algorithms of very high accuracy. For this
reason the programs should be looked upon as a stimulus for writing more advanced
software employing Taylor series better able to compete with programs using other
methods. An attempt in this direction is TKSL [8], a program the results of which
will be dealt with.",
  address="IEEE Computer Society",
  booktitle="Proceedings of Third Asia International Conference on Modelling and Simulation",
  chapter="30213",
  edition="NEUVEDEN",
  howpublished="print",
  institution="IEEE Computer Society",
  year="2009",
  month="may",
  pages="206--211",
  publisher="IEEE Computer Society",
  type="conference paper"
}