Parallel solution of higher order differential equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F16%3A86098839" target="_blank" >RIV/61989100:27740/16:86098839 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216305:26230/16:PU122416

Výsledek na webu

<a href="http://dx.doi.org/10.1109/HPCSim.2016.7568350" target="_blank" >http://dx.doi.org/10.1109/HPCSim.2016.7568350</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/HPCSim.2016.7568350" target="_blank" >10.1109/HPCSim.2016.7568350</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Parallel solution of higher order differential equations

Popis výsledku v původním jazyce

The paper focuses on a mathematical approach which uses Modern Taylor Series Method (MTSM) for solving differential equations in a parallel way. Even though this method is not much preferred in the literature, some experimental calculations have shown and verified that the accuracy and stability of the MTSM exceeds the currently used algorithms for solving differential equations. Further, the MTSM has properties suitable for parallel processing, i.e. many independent calculations. The MTSM allows these calculations to be performed independently on several processors using basic mathematical operations. Hardware representation of these operations and their principle are discussed in this paper. Generally, the MTSM can only solve systems of ordinary differential equations (ODEs) that are formed as initial value problems (IVPs). Therefore, this paper also presents methods for solving higher order differential equations, PDEs and their transformations to the corresponding systems of ODEs (IVPs). Effectiveness of hardware implementation of the MTSM is also discussed in this paper, e.g. implementation on FPGA. In many cases, the MTSM obtains results faster than the commonly used Runge-Kutta methods. (C) 2016 IEEE.

Název v anglickém jazyce

Parallel solution of higher order differential equations

Popis výsledku anglicky

The paper focuses on a mathematical approach which uses Modern Taylor Series Method (MTSM) for solving differential equations in a parallel way. Even though this method is not much preferred in the literature, some experimental calculations have shown and verified that the accuracy and stability of the MTSM exceeds the currently used algorithms for solving differential equations. Further, the MTSM has properties suitable for parallel processing, i.e. many independent calculations. The MTSM allows these calculations to be performed independently on several processors using basic mathematical operations. Hardware representation of these operations and their principle are discussed in this paper. Generally, the MTSM can only solve systems of ordinary differential equations (ODEs) that are formed as initial value problems (IVPs). Therefore, this paper also presents methods for solving higher order differential equations, PDEs and their transformations to the corresponding systems of ODEs (IVPs). Effectiveness of hardware implementation of the MTSM is also discussed in this paper, e.g. implementation on FPGA. In many cases, the MTSM obtains results faster than the commonly used Runge-Kutta methods. (C) 2016 IEEE.

Druh

D - Stať ve sborníku

CEP obor

IN - Informatika

OECD FORD obor

—

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the 2016 International Conference on High Performance Computing &amp; Simulation (HPCS 2016)

ISBN

978-1-5090-2088-1

ISSN

—

e-ISSN

—

Počet stran výsledku

8

Strana od-do

302-309

Název nakladatele

IEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA

Místo vydání

345 E 47TH ST, NEW YORK, NY 10017 USA

Místo konání akce

Innsbruck

Datum konání akce

18. 7. 2016

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000389590600042