Publication Details

Taylor Series Based Solution of Linear ODE Systems and MATLAB Solvers Comparison

ŠÁTEK Václav, KOCINA Filip, KUNOVSKÝ Jiří and SCHIRRER Alexander. Taylor Series Based Solution of Linear ODE Systems and MATLAB Solvers Comparison. In: MATHMOD VIENNA 2015 - 8th Vienna Conference on Mathematical Modelling. ARGESIM REPORT No. 44. Vienna: ARGE Simulation News, 2015, pp. 693-694. ISBN 978-3-901608-46-9. Available from: http://www.sciencedirect.com/science/article/pii/S2405896315002116
Czech title
Řešení lineárních systému obyčejných diferenciálních rovnic s využitím Taylorova rozvoje a porovnání s MATLAB řešíči
Type
conference paper
Language
english
Authors
Šátek Václav, Ing., Ph.D. (DITS FIT BUT)
Kocina Filip, Ing., Ph.D. (DITS FIT BUT)
Kunovský Jiří, doc. Ing., CSc. (DITS FIT BUT)
Schirrer Alexander, doc. Dr. Ing. (TU-Wien)
URL
Keywords

Ordinary differential equations, Initial value problems, Taylor series, MATLAB

Abstract

The Modern Taylor Series Method (MTSM) is employed here to solve initial value problems of linear ordinary differential equations. An automatic computation of higher Taylor series terms and an efficient, vectorized coding of explicit and implicit schemes enables a very fast computation of the solution to specified accuracy. For a set of benchmark problems from literature, the MTSM significantly outperforms standard solvers.
Finally, ideas of parallelizing the MTSM computations are discussed.

Published
2015
Pages
693-694
Proceedings
MATHMOD VIENNA 2015 - 8th Vienna Conference on Mathematical Modelling
Series
ARGESIM REPORT No. 44
Conference
MATHMOD 2015 - 8th Vienna International Conference on Mathematical Modelling, Vienna, AT
ISBN
978-3-901608-46-9
Publisher
ARGE Simulation News
Place
Vienna, AT
DOI
10.1016/j.ifacol.2015.05.210
EID Scopus
2-s2.0-84954152963
BibTeX 
@INPROCEEDINGS{FITPUB10795,
   author = "V\'{a}clav \v{S}\'{a}tek and Filip Kocina and Ji\v{r}\'{i} Kunovsk\'{y} and Alexander Schirrer",
   title = "Taylor Series Based Solution of Linear ODE Systems and MATLAB Solvers Comparison",
   pages = "693--694",
   booktitle = "MATHMOD VIENNA 2015 - 8th Vienna Conference on Mathematical Modelling",
   series = "ARGESIM REPORT No. 44",
   year = 2015,
   location = "Vienna, AT",
   publisher = "ARGE Simulation News",
   ISBN = "978-3-901608-46-9",
   doi = "10.1016/j.ifacol.2015.05.210",
   language = "english",
   url = "https://www.fit.vut.cz/research/publication/10795"
}
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