Publication result detail

Taylor Series Based Solution of Nonlinear-quadratic ODE Systems

ŠÁTEK, V.; VEIGEND, P.; NEČASOVÁ, G.

Original Title

Taylor Series Based Solution of Nonlinear-quadratic ODE Systems

English Title

Taylor Series Based Solution of Nonlinear-quadratic ODE Systems

Type

Paper in proceedings outside WoS and Scopus

Original Abstract

The paper deals with possibilities of numerical solution of special type of nonlinear-quadratic systems of Initial Value Problems of Ordinary Di erential Equations (ODEs). The research is focused on higher order and variable step size method based on Taylor series
computation. Taylor series method for solving di erential equations represents a non-traditional way of a numerical solution.
The e ffective implementation of Modern Taylor Series Method (MTSM) in MATLAB software is introduced. The MTSM is based on automatic and recurrent calculation of higher Taylor series terms. The computation time and accuracy of our approach are compared with that of MATLAB ode solvers on a set of nonlinear-quadratic ODE systems coming from real world technical problems.

English abstract

The paper deals with possibilities of numerical solution of special type of nonlinear-quadratic systems of Initial Value Problems of Ordinary Di erential Equations (ODEs). The research is focused on higher order and variable step size method based on Taylor series
computation. Taylor series method for solving di erential equations represents a non-traditional way of a numerical solution.
The e ffective implementation of Modern Taylor Series Method (MTSM) in MATLAB software is introduced. The MTSM is based on automatic and recurrent calculation of higher Taylor series terms. The computation time and accuracy of our approach are compared with that of MATLAB ode solvers on a set of nonlinear-quadratic ODE systems coming from real world technical problems.

Keywords

Continuous systems, Ordinary di erential equations, Initial value problems, Taylor series, MATLAB

Key words in English

Continuous systems, Ordinary di erential equations, Initial value problems, Taylor series, MATLAB

Authors

ŠÁTEK, V.; VEIGEND, P.; NEČASOVÁ, G.

Released

23.02.2018

Publisher

ARGE Simulation News

Location

Vienna

ISBN

978-3-901608-91-9

Book

MATHMOD VIENNA 2018 - 9th Vienna International Conference on Mathematical Modelling

Pages from

99

Pages to

100

Pages count

2

BibTex

@inproceedings{BUT168458,
  author="Václav {Šátek} and Petr {Veigend} and Gabriela {Nečasová}",
  title="Taylor Series Based Solution of Nonlinear-quadratic ODE Systems",
  booktitle="MATHMOD VIENNA 2018 - 9th Vienna International Conference on Mathematical Modelling",
  year="2018",
  pages="99--100",
  publisher="ARGE Simulation News",
  address="Vienna",
  doi="10.11128/arep.55",
  isbn="978-3-901608-91-9"
}