Publication result detail

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

ŠÁTEK, V.; KOCINA, F.; KUNOVSKÝ, J.; SCHIRRER, A.

Original Title

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

English Title

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

Type

Paper in proceedings (conference paper)

Original 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.

English 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.

Keywords

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

Key words in English

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

Authors

ŠÁTEK, V.; KOCINA, F.; KUNOVSKÝ, J.; SCHIRRER, A.

RIV year

2016

Released

18.02.2015

Publisher

ARGE Simulation News

Location

Vienna

ISBN

978-3-901608-46-9

Book

MATHMOD VIENNA 2015 - 8th Vienna Conference on Mathematical Modelling

Edition

ARGESIM REPORT No. 44

Pages from

693

Pages to

694

Pages count

2

URL

http://www.sciencedirect.com/science/article/pii/S2405896315002116

BibTex

@inproceedings{BUT119809,
  author="Václav {Šátek} and Filip {Kocina} and Jiří {Kunovský} and Alexander {Schirrer}",
  title="Taylor Series Based Solution of Linear ODE Systems and MATLAB Solvers Comparison",
  booktitle="MATHMOD VIENNA 2015 - 8th Vienna Conference on Mathematical Modelling",
  year="2015",
  series="ARGESIM REPORT No. 44",
  pages="693--694",
  publisher="ARGE Simulation News",
  address="Vienna",
  doi="10.1016/j.ifacol.2015.05.210",
  isbn="978-3-901608-46-9",
  url="http://www.sciencedirect.com/science/article/pii/S2405896315002116"
}

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