Detail publikace

Technical Initial Problems and Automatic Transformation

KALUŽA, V. KUNOVSKÝ, J. SEHNALOVÁ, P. KOPŘIVA, J.

Originální název

Technical Initial Problems and Automatic Transformation

Anglický název

Technical Initial Problems and Automatic Transformation

Jazyk

en

Originální abstrakt

In this paper an outline is given of historical and current developments in the application of recurrent Taylor series to the integration of systems of ordinary differential equations. Then an extremely accurate and fast method for the numerical solution of ordinary differential equations is presented. In general Taylor series method is not included or 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 finding integration algorithms of very high accuracy. For this reason such 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, a program the results of which will be dealt with.

Anglický abstrakt

In this paper an outline is given of historical and current developments in the application of recurrent Taylor series to the integration of systems of ordinary differential equations. Then an extremely accurate and fast method for the numerical solution of ordinary differential equations is presented. In general Taylor series method is not included or 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 finding integration algorithms of very high accuracy. For this reason such 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, a program the results of which will be dealt with.

Dokumenty

BibTex


@inproceedings{BUT33802,
  author="Vlastimil {Kaluža} and Jiří {Kunovský} and Pavla {Sehnalová} and Jan {Kopřiva}",
  title="Technical Initial Problems and Automatic Transformation",
  annote="In this paper an outline is given of historical and current developments in the
application of recurrent Taylor series to the integration of systems of ordinary
differential equations. Then an extremely accurate and fast method for the
numerical solution of ordinary differential equations is presented.
In general Taylor series method is not included or 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 finding integration algorithms of very high accuracy. For this reason
such 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, a program the results of which
will be dealt with.",
  address="IEEE Computer Society",
  booktitle="2009 International Conference on Computational Intelligence, Modelling and Simulation",
  chapter="33802",
  edition="NEUVEDEN",
  howpublished="print",
  institution="IEEE Computer Society",
  year="2009",
  month="september",
  pages="75--80",
  publisher="IEEE Computer Society",
  type="conference paper"
}