KUNOVSKÝ Jiří, ŠÁTEK Václav, NEČASOVÁ Gabriela, VEIGEND Petr and KOCINA Filip. The Positive Properties of Taylor Series Method. In: Proceedings of the 13th International Conference Informatics' 2015. Poprad: Institute of Electrical and Electronics Engineers, 2015, pp. 156160. ISBN 9781467398671. 
Publication language:  english 

Original title:  The Positive Properties of Taylor Series Method 

Title (cs):  Pozitivní vlastnosti metody Taylorovy řady 

Pages:  156160 

Proceedings:  Proceedings of the 13th International Conference Informatics' 2015 

Conference:  Informatics 2015  13th International Scientific Conference on Informatics 

Place:  Poprad, SK 

Year:  2015 

ISBN:  9781467398671 

DOI:  10.1109/Informatics.2015.7377825 

Publisher:  Institute of Electrical and Electronics Engineers 

Keywords 

Taylor Series Method, Ordinary Differential Equations, Parallel Computation

Annotation 

The paper deals with the computation which is based on an original mathematical method. This method uses the Taylor series for solving differential equations in a nontraditional way.
The Modern Taylor Series is based on a recurrent calculation of the Taylor series terms for each time interval. Thus the complicated calculation of higher order derivatives (much criticised in the literature) need not be performed but rather the value of each Taylor series term is numerically calculated. Solving the convolution operations is another typical algorithm used.
An important part of the method is an automatic integration order setting, i.e. using as many Taylor series terms as the defined accuracy requires. Thus it is usual that the computation uses different numbers of Taylor series terms for different steps of constant length.
An automatic transformation of the original problem is a necessary part of the Modern Taylor Series Method. The original system of differential equations is automatically transformed to a polynomial form, i.e. to a form suitable for easily calculating the Taylor series forms using recurrent formulae.
The "Modern Taylor Series Method" also has some properties very favourable for parallel processing. Many calculation operations are independent making it possible to perform the calculations independently using separate processors of parallel computing systems. 
BibTeX: 

@INPROCEEDINGS{
author = {Ji{\v{r}}{\'{i}} Kunovsk{\'{y}} and V{\'{a}}clav
{\v{S}}{\'{a}}tek and Gabriela
Ne{\v{c}}asov{\'{a}} and Petr Veigend and Filip
Kocina},
title = {The Positive Properties of Taylor Series Method},
pages = {156160},
booktitle = {Proceedings of the 13th International Conference
Informatics' 2015},
year = 2015,
location = {Poprad, SK},
publisher = {Institute of Electrical and Electronics Engineers},
ISBN = {9781467398671},
doi = {10.1109/Informatics.2015.7377825},
language = {english},
url = {http://www.fit.vutbr.cz/research/view_pub.php?id=10923}
} 