The Positive Properties of Taylor Series Method

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26230%2F15%3APU117260" target="_blank" >RIV/00216305:26230/15:PU117260 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1109/Informatics.2015.7377825" target="_blank" >http://dx.doi.org/10.1109/Informatics.2015.7377825</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/Informatics.2015.7377825" target="_blank" >10.1109/Informatics.2015.7377825</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Positive Properties of Taylor Series Method

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The Positive Properties of Taylor Series Method

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: Centrum excelence IT4Innovations</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Proceedings of the 13th International Conference Informatics' 2015

ISBN

978-1-4673-9867-1

ISSN

—

e-ISSN

—

Počet stran výsledku

6

Strana od-do

156-160

Název nakladatele

Institute of Electrical and Electronics Engineers

Místo vydání

Poprad

Místo konání akce

Poprad

Datum konání akce

18. 11. 2015

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000380535000028