An Algorithm to Solve Systems of Nonlinear Differential-Algebraic Equations With Extraordinary Efficiency Even at High Demanded Precisions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00355588" target="_blank" >RIV/68407700:21230/21:00355588 - isvavai.cz</a>

Výsledek na webu

—

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

An Algorithm to Solve Systems of Nonlinear Differential-Algebraic Equations With Extraordinary Efficiency Even at High Demanded Precisions

Popis výsledku v původním jazyce

There are many situations when systems of nonlinear differential algebraic equations need to be solved with extraordinary precision. A steady-state analysis (determining the steady-state period of a system after a transient) is a typical case because a vector of unknown variables should be exactly the same after a numerical integration on the period-long interval. Therefore, we need to develop such kinds of numerical algorithms that are computationally effective, even at very high requirements on the accuracy of the results. In the paper, an efficient and reliable algorithm for solving systems of algebraic-differential nonlinear equations is characterized first. Unlike in other cases, the procedure is based on a sophisticated arrangement of the Newton interpolation polynomial (i.e., not the Lagrange one). This feature provides greater flexibility in rapidly changing interpolation step sizes and orders during numerical integration. At the end of the paper, two complicated examples are presented to demonstrate that the algorithm's computational requirement is quite low, even at very high demands on the accuracy of results.

Název v anglickém jazyce

An Algorithm to Solve Systems of Nonlinear Differential-Algebraic Equations With Extraordinary Efficiency Even at High Demanded Precisions

Popis výsledku anglicky

There are many situations when systems of nonlinear differential algebraic equations need to be solved with extraordinary precision. A steady-state analysis (determining the steady-state period of a system after a transient) is a typical case because a vector of unknown variables should be exactly the same after a numerical integration on the period-long interval. Therefore, we need to develop such kinds of numerical algorithms that are computationally effective, even at very high requirements on the accuracy of the results. In the paper, an efficient and reliable algorithm for solving systems of algebraic-differential nonlinear equations is characterized first. Unlike in other cases, the procedure is based on a sophisticated arrangement of the Newton interpolation polynomial (i.e., not the Lagrange one). This feature provides greater flexibility in rapidly changing interpolation step sizes and orders during numerical integration. At the end of the paper, two complicated examples are presented to demonstrate that the algorithm's computational requirement is quite low, even at very high demands on the accuracy of results.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

20201 - Electrical and electronic engineering

Projekt

<a href="/cs/project/GA20-26849S" target="_blank" >GA20-26849S: Nové algoritmy pro přesnou, efektivní a robustní analýzu rozsáhlých systémů</a><br>

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proc. of the 2021 International Conference on Computational Science and Computational Intelligence (CSCI’21)

ISBN

978-1-60132-515-0

ISSN

—

e-ISSN

—

Počet stran výsledku

5

Strana od-do

1-5

Název nakladatele

IEEE Computer Society

Místo vydání

Los Alamitos

Místo konání akce

Las Vegas

Datum konání akce

15. 12. 2021

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—