Rigorous Integration of Non-Linear Ordinary Differential Equations in Chebyshev Basis
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Rigorous Integration of Non-Linear Ordinary Differential Equations in Chebyshev Basis
Original language description
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).
Czech name
—
Czech description
—
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
—
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Numerical Algorithms
ISSN
1017-1398
e-ISSN
—
Volume of the periodical
69
Issue of the periodical within the volume
1
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
23
Pages from-to
183-205
UT code for WoS article
000353508200011
EID of the result in the Scopus database
2-s2.0-84940235016