Publication result detail

Technical Initial Problems and Automatic Transformation

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

Original Title

Technical Initial Problems and Automatic Transformation

English Title

Technical Initial Problems and Automatic Transformation

Type

Paper in proceedings outside WoS and Scopus

Original Abstract

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.

English abstract

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.

Keywords

Taylor series method, differential equations, TKSL, numerical method, order of Taylor series method

Key words in English

Taylor series method, differential equations, TKSL, numerical method, order of Taylor series method

Authors

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

RIV year

2010

Released

07.09.2009

Publisher

IEEE Computer Society

Location

Brno

ISBN

978-0-7695-3795-5

Book

2009 International Conference on Computational Intelligence, Modelling and Simulation

Pages from

75

Pages to

80

Pages count

6

Full text in the Digital Library

http://hdl.handle.net/

BibTex

@inproceedings{BUT33802,
  author="Vlastimil {Kaluža} and Jiří {Kunovský} and Pavla {Sehnalová} and Jan {Kopřiva}",
  title="Technical Initial Problems and Automatic Transformation",
  booktitle="2009 International Conference on Computational Intelligence, Modelling and Simulation",
  year="2009",
  pages="75--80",
  publisher="IEEE Computer Society",
  address="Brno",
  isbn="978-0-7695-3795-5"
}