Detail výsledku

Initial Problems with Polynomials on Right-hand Sides

KALUŽA, V.; KRAUS, M.; KUNOVSKÝ, J.; ŠÁTEK, V. Initial Problems with Polynomials on Right-hand Sides. In Proceedings of Third Asia International Conference on Modelling and Simulation. Bandung/Bali: IEEE Computer Society, 2009. p. 182-187. ISBN: 978-0-7695-3648-4.
Typ
článek ve sborníku konference
Jazyk
anglicky
Autoři
Kaluža Vlastimil, Ing., UITS (FIT)
Kraus Michal, Ing., Ph.D., UITS (FIT)
Kunovský Jiří, doc. Ing., CSc., UITS (FIT)
Šátek Václav, Ing., Ph.D., UITS (FIT)
Abstrakt

As long as 250 years ago the method of Taylor series was already well developed. Since then the application of Taylor series has become a standard concept in numerical analysis. Their ability of approximating functions arbitrarily close under certain conditions makes them, at least theoretically, an ideal tool for the integration of differential equations.
Before the appearance of digital computers the analytical determination of Taylor series coefficients, i.e. the calculation of higher derivatives, was regarded as too complicated in most cases. In many modern text books [3], [4] on numerical or applied mathematics has even been stated that Taylor series, although theoretically and conceptually very interesting, can only be applied as implementation in very special cases, since a general purpose integration algorithm is too complicated or even impossible.
In this paper an outline is presented of establishing Taylor series coefficients of initial problems with polynomials on right-hand sides. The application of recurrent Taylor series to the integration of systems of ordinary differential equations is discused. The software TKSL for the solution of initial value problems by means of recurrent Taylor series has been developed and many positive results have been obtained [5]. TKSL is available for those interested.

Klíčová slova

ordinary differential equations, TKSL, Taylor series method

Rok
2009
Strany
182–187
Sborník
Proceedings of Third Asia International Conference on Modelling and Simulation
Konference
Third Asia International Conference on Modelling & Simulation
ISBN
978-0-7695-3648-4
Vydavatel
IEEE Computer Society
Místo
Bandung/Bali
UT WoS
000271349800032
BibTeX
@inproceedings{BUT33784,
  author="Vlastimil {Kaluža} and Michal {Kraus} and Jiří {Kunovský} and Václav {Šátek}",
  title="Initial Problems with Polynomials on Right-hand Sides",
  booktitle="Proceedings of Third Asia International Conference on Modelling and Simulation",
  year="2009",
  pages="182--187",
  publisher="IEEE Computer Society",
  address="Bandung/Bali",
  isbn="978-0-7695-3648-4"
}
Projekty
Výzkum informačních technologií z hlediska bezpečnosti, MŠMT, Institucionální prostředky SR ČR (např. VZ, VC), MSM0021630528, zahájení: 2007-01-01, ukončení: 2013-12-31, řešení
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