Conference paper

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. 156-160. ISBN 978-1-4673-9867-1.
Publication language:english
Original title:The Positive Properties of Taylor Series Method
Title (cs):Pozitivní vlastnosti metody Taylorovy řady
Pages:156-160
Proceedings:Proceedings of the 13th International Conference Informatics' 2015
Conference:Informatics 2015 - 13th International Scientific Conference on Informatics
Place:Poprad, SK
Year:2015
ISBN:978-1-4673-9867-1
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 non-traditional 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 = {156--160},
   booktitle = {Proceedings of the 13th International Conference
	Informatics' 2015},
   year = {2015},
   location = {Poprad, SK},
   publisher = {Institute of Electrical and Electronics Engineers},
   ISBN = {978-1-4673-9867-1},
   language = {english},
   url = {http://www.fit.vutbr.cz/research/view_pub.php?id=10923}
}

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