Detail publikace

# The Positive Properties of Taylor Series Method

KUNOVSKÝ, J. ŠÁTEK, V. NEČASOVÁ, G. VEIGEND, P. KOCINA, F.

Originální název

The Positive Properties of Taylor Series Method

Anglický název

The Positive Properties of Taylor Series Method

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

Dokumenty

BibTex

``````
@inproceedings{BUT120377,
author="Jiří {Kunovský} and Václav {Šátek} and Gabriela {Nečasová} and Petr {Veigend} and Filip {Kocina}",
title="The Positive Properties of Taylor Series Method",
annote="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.",
address="Institute of Electrical and Electronics Engineers",
booktitle="Proceedings of the 13th International Conference Informatics' 2015",
chapter="120377",
doi="10.1109/Informatics.2015.7377825",
edition="NEUVEDEN",
howpublished="print",
institution="Institute of Electrical and Electronics Engineers",
year="2015",
month="november",
pages="156--160",
publisher="Institute of Electrical and Electronics Engineers",
type="conference paper"
}``````