A ⋆-product solver with spectral accuracy for non-autonomous ordinary differential equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10474089" target="_blank" >RIV/00216208:11320/23:10474089 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1002/pamm.202200050" target="_blank" >https://doi.org/10.1002/pamm.202200050</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/pamm.202200050" target="_blank" >10.1002/pamm.202200050</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A ⋆-product solver with spectral accuracy for non-autonomous ordinary differential equations

Popis výsledku v původním jazyce

A new method for solving non-autonomous ordinary differential equations is proposed, the method achieves spectral accuracy. It is based on a new result which expresses the solution of such ODEs as an element in the so called STAR OPERATOR-algebra. This algebra is equipped with a product, the STAR OPERATOR-product, which is the integral over the usual product of two bivariate distributions. Expanding the bivariate distributions in bases of Legendre polynomials leads to a discretization of the STAR OPERATOR-product and this allows for the solution to be approximated by a vector that is obtained by solving a linear system of equations. The effectiveness of this approach is illustrated with numerical experiments.

Název v anglickém jazyce

A ⋆-product solver with spectral accuracy for non-autonomous ordinary differential equations

Popis výsledku anglicky

A new method for solving non-autonomous ordinary differential equations is proposed, the method achieves spectral accuracy. It is based on a new result which expresses the solution of such ODEs as an element in the so called STAR OPERATOR-algebra. This algebra is equipped with a product, the STAR OPERATOR-product, which is the integral over the usual product of two bivariate distributions. Expanding the bivariate distributions in bases of Legendre polynomials leads to a discretization of the STAR OPERATOR-product and this allows for the solution to be approximated by a vector that is obtained by solving a linear system of equations. The effectiveness of this approach is illustrated with numerical experiments.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název statě ve sborníku

92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)

ISBN

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ISSN

1617-7061

e-ISSN

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Počet stran výsledku

6

Strana od-do

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Název nakladatele

John Wiley &amp; Sons, Inc.

Místo vydání

Neuveden

Místo konání akce

RWTH Aachen University

Datum konání akce

15. 8. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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