Conference paperKALUŽA Vlastimil, KUNOVSKÝ Jiří, SEHNALOVÁ Pavla and KOPŘIVA Jan. Technical Initial Problems and Automatic Transformation. In: 2009 International Conference on Computational Intelligence, Modelling and Simulation. Brno: IEEE Computer Society, 2009, pp. 7580. ISBN 9780769537955.  Publication language:  english 

Original title:  Technical Initial Problems and Automatic Transformation 

Title (cs):  Technické počáteční problémy a automatická transformace 

Pages:  7580 

Proceedings:  2009 International Conference on Computational Intelligence, Modelling and Simulation 

Conference:  International Conference on Computer Modelling and Simulation  CSSim 2009 

Place:  Brno, CZ 

Year:  2009 

ISBN:  9780769537955 

Publisher:  IEEE Computer Society 

Keywords 

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

Annotation 

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.

BibTeX: 

@INPROCEEDINGS{
author = {Vlastimil Kalu{\v{z}}a and Ji{\v{r}}{\'{i}} Kunovsk{\'{y}}
and Pavla Sehnalov{\'{a}} and Jan Kop{\v{r}}iva},
title = {Technical Initial Problems and Automatic Transformation},
pages = {7580},
booktitle = {2009 International Conference on Computational Intelligence,
Modelling and Simulation},
year = {2009},
location = {Brno, CZ},
publisher = {IEEE Computer Society},
ISBN = {9780769537955},
language = {english},
url = {http://www.fit.vutbr.cz/research/view_pub.php?id=9050}
} 
