Conference paper

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. Vienna: ARGE Simulation News, 2015, pp. 693-694. ISBN 978-3-901608-46-9. Available from: http://www.sciencedirect.com/science/article/pii/S2405896315002116
Publication language:english
Original title:Taylor Series Based Solution of Linear ODE Systems and MATLAB Solvers Comparison
Title (cs):Řešení lineárních systému obyčejných diferenciálních rovnic s využitím Taylorova rozvoje a porovnání s MATLAB řešíči
Pages:693-694
Proceedings:MATHMOD VIENNA 2015 - 8th Vienna Conference on Mathematical Modelling
Conference:MATHMOD 2015 - 8th Vienna International Conference on Mathematical Modelling
Series:ARGESIM REPORT No. 44
Place:Vienna, AT
Year:2015
URL:http://www.sciencedirect.com/science/article/pii/S2405896315002116
ISBN:978-3-901608-46-9
Publisher:ARGE Simulation News
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Keywords
Ordinary differential equations, Initial value problems, Taylor series, MATLAB
Annotation
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.
BibTeX:
@INPROCEEDINGS{
   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},
   language = {english},
   url = {http://www.fit.vutbr.cz/research/view_pub.php?id=10795}
}

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