Publication result detail

Taylor series based numerical integration method for solution of nonlinear problems with division

VEIGEND, P.; NEČASOVÁ, G.; ŠÁTEK, V.

Original Title

Taylor series based numerical integration method for solution of nonlinear problems with division

English Title

Taylor series based numerical integration method for solution of nonlinear problems with division

Type

Paper in proceedings (conference paper)

Original Abstract

Most methods for solving ordinary differential equations use a limited order to calculate the results. The higher order method presented in this article can use as many terms of the Taylor series as necessary to obtain a stable and accurate solution. The solution using this method (particularly for nonlinear problems) can be quite complex. The aim of this article is to compare several ways of expressing the operation division in the nonlinear problems of ordinary differential equations and compare these approaches with one another and to the state-of-the-art solvers in MATLAB software.

English abstract

Most methods for solving ordinary differential equations use a limited order to calculate the results. The higher order method presented in this article can use as many terms of the Taylor series as necessary to obtain a stable and accurate solution. The solution using this method (particularly for nonlinear problems) can be quite complex. The aim of this article is to compare several ways of expressing the operation division in the nonlinear problems of ordinary differential equations and compare these approaches with one another and to the state-of-the-art solvers in MATLAB software.

Keywords

Taylor series method, MATLAB, initial value problems, nonlinear ordinary differential equations

Key words in English

Taylor series method, MATLAB, initial value problems, nonlinear ordinary differential equations

Authors

VEIGEND, P.; NEČASOVÁ, G.; ŠÁTEK, V.

RIV year

2026

Released

18.07.2025

Publisher

Institute of Electrical and Electronics Engineers

Location

Poprad

ISBN

979-8-3503-8768-1

Book

2024 IEEE 17th International Scientific Conference on Informatics Proceedings

Pages from

421

Pages to

426

Pages count

6

BibTex

@inproceedings{BUT193303,
  author="Petr {Veigend} and Gabriela {Nečasová} and Václav {Šátek}",
  title="Taylor series based numerical integration method for solution of nonlinear problems with division",
  booktitle="2024 IEEE 17th International Scientific Conference on Informatics Proceedings",
  year="2025",
  pages="421--426",
  publisher="Institute of Electrical and Electronics Engineers",
  address="Poprad",
  doi="10.1109/Informatics62280.2024.10900903",
  isbn="979-8-3503-8768-1"
}