Conference paperDROZDOVÁ Martina, KOPŘIVA Jan, KUNOVSKÝ Jiří and PINDRYČ Milan. Methodology of the Taylor Series Based Computations. In: Proceedings of Third Asia International Conference on Modelling and Simulation. Bandung/Bali: IEEE Computer Society, 2009, pp. 206211. ISBN 9780769536484.  Publication language:  english 

Original title:  Methodology of the Taylor Series Based Computations 

Title (cs):  Metodologie výpočtu pomocí Taylorovy řady 

Pages:  206211 

Proceedings:  Proceedings of Third Asia International Conference on Modelling and Simulation 

Conference:  Third Asia International Conference on Modelling & Simulation 

Place:  Bandung/Bali, ID 

Year:  2009 

ISBN:  9780769536484 

Publisher:  IEEE Computer Society 

Keywords 

ordinary differential equations, TKSL, Taylor series method, Fourier analysis 
Annotation 

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{
author = {Martina Drozdov{\'{a}} and Jan Kop{\v{r}}iva and
Ji{\v{r}}{\'{i}} Kunovsk{\'{y}} and Milan Pindry{\v{c}}},
title = {Methodology of the Taylor Series Based Computations},
pages = {206211},
booktitle = {Proceedings of Third Asia International Conference on
Modelling and Simulation},
year = {2009},
location = {Bandung/Bali, ID},
publisher = {IEEE Computer Society},
ISBN = {9780769536484},
language = {english},
url = {http://www.fit.vutbr.cz/research/view_pub.php?id=8964}
} 
