Rigorous Integration of Non-Linear Ordinary Differential Equations in Chebyshev Basis

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F15%3A00442870" target="_blank" >RIV/67985807:_____/15:00442870 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s11075-014-9889-x" target="_blank" >http://dx.doi.org/10.1007/s11075-014-9889-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11075-014-9889-x" target="_blank" >10.1007/s11075-014-9889-x</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Rigorous Integration of Non-Linear Ordinary Differential Equations in Chebyshev Basis

Popis výsledku v původním jazyce

In this paper, we introduce a new approach to multiple step verified integration of non-linear ordinary differential equations. The approach is based on the technique of a Taylor model integration, however, a novel method is introduced to suppress the wrapping effect over several integration steps. This method is simpler and more robust compared to the known methods. It allows more general inputs, while it does not require rigorous matrix inversion. Moreover, our integration algorithm allows the use ofvarious types of underlying function enclosures. We present rigorous arithmetic operations with function enclosures based on the truncated Chebyshev series. Computational experiments are used to show the wrapping effect suppression of our method and to compare integration algorithm that uses Chebyshev function enclosures with the existing algorithms that use function enclosures based on the truncated Taylor series (Taylor models).

Název v anglickém jazyce

Rigorous Integration of Non-Linear Ordinary Differential Equations in Chebyshev Basis

Popis výsledku anglicky

In this paper, we introduce a new approach to multiple step verified integration of non-linear ordinary differential equations. The approach is based on the technique of a Taylor model integration, however, a novel method is introduced to suppress the wrapping effect over several integration steps. This method is simpler and more robust compared to the known methods. It allows more general inputs, while it does not require rigorous matrix inversion. Moreover, our integration algorithm allows the use ofvarious types of underlying function enclosures. We present rigorous arithmetic operations with function enclosures based on the truncated Chebyshev series. Computational experiments are used to show the wrapping effect suppression of our method and to compare integration algorithm that uses Chebyshev function enclosures with the existing algorithms that use function enclosures based on the truncated Taylor series (Taylor models).

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

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

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Numerical Algorithms

ISSN

1017-1398

e-ISSN

—

Svazek periodika

69

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

23

Strana od-do

183-205

Kód UT WoS článku

000353508200011

EID výsledku v databázi Scopus

2-s2.0-84940235016