Numerical Solution of the Integro-Differential Equation of the Transient Response in the Electric Circuits: Application of the Modified Euler's Method and Numerical Quadrature

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216275%3A25530%2F25%3A39924137" target="_blank" >RIV/00216275:25530/25:39924137 - isvavai.cz</a>

Výsledek na webu

<a href="https://pubs.aip.org/aip/acp/article-abstract/3315/1/400014/3363161/Numerical-solution-of-the-integro-differential?redirectedFrom=fulltext" target="_blank" >https://pubs.aip.org/aip/acp/article-abstract/3315/1/400014/3363161/Numerical-solution-of-the-integro-differential?redirectedFrom=fulltext</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/5.0286612" target="_blank" >10.1063/5.0286612</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Numerical Solution of the Integro-Differential Equation of the Transient Response in the Electric Circuits: Application of the Modified Euler's Method and Numerical Quadrature

Popis výsledku v původním jazyce

Integro-differencial equations plays an eminent role in description of various physical, chemical, and biological phenomena and systems, especially of a dynamic nature. They are used in construction of simulation models that try to mathematically solve the behavior and response of real events, occurring in diverse systems, completely or with a certain degree of approximation. Thus, it is of a high importance to solve them. However, in most cases, analytical approaches fail and therefore, numerical methods are necessary to employ to find their solution. In the present study, we focus on a problem of solving the integro-differential equation for the transient phenomena in a serial RLC circuit. We present a numerical method based on the explicit Euler protocol and compare its results with those from the analytical solutions in terms of the error development. These findings could stimulate future work, possibly exploiting other Runge-Kutta methods or multistep methods with different quadrature rules.

Název v anglickém jazyce

Numerical Solution of the Integro-Differential Equation of the Transient Response in the Electric Circuits: Application of the Modified Euler's Method and Numerical Quadrature

Popis výsledku anglicky

Integro-differencial equations plays an eminent role in description of various physical, chemical, and biological phenomena and systems, especially of a dynamic nature. They are used in construction of simulation models that try to mathematically solve the behavior and response of real events, occurring in diverse systems, completely or with a certain degree of approximation. Thus, it is of a high importance to solve them. However, in most cases, analytical approaches fail and therefore, numerical methods are necessary to employ to find their solution. In the present study, we focus on a problem of solving the integro-differential equation for the transient phenomena in a serial RLC circuit. We present a numerical method based on the explicit Euler protocol and compare its results with those from the analytical solutions in terms of the error development. These findings could stimulate future work, possibly exploiting other Runge-Kutta methods or multistep methods with different quadrature rules.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název statě ve sborníku

AIP Conference Proceedings, Volume 3315

ISBN

978-0-7354-5245-9

ISSN

0094-243X

e-ISSN

1551-7616

Počet stran výsledku

4

Strana od-do

1

Název nakladatele

AIP publishing

Místo vydání

New York

Místo konání akce

Heraklion

Datum konání akce

11. 9. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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