Publication Details

Solving linear and nonlinear problems using Taylor Series Method

VEIGEND, P.; NEČASOVÁ, G.; ŠÁTEK, V. Solving linear and nonlinear problems using Taylor Series Method. Open Computer Science, 2024, vol. 14, no. 1, p. 1-15. ISSN: 2299-1093.

Czech title

Řešení lineárních a nelineárních úloh pomocí numerické metody založené na Taloyorově polynomu

Type

journal article

Language

English

Authors

Veigend Petr, Ing., Ph.D. (DITS)
Nečasová Gabriela, Ing., Ph.D. (DITS)
Šátek Václav, Ing., Ph.D. (DITS)

URL

https://www.degruyter.com/document/doi/10.1515/comp-2024-0005/html

Keywords

initial value problems, Taylor series, MTSM, MATLAB, PETSc

Abstract

This paper focuses on the Taylor-series-based high-order numerical integration
method. Linear and nonlinear systems of ordinary differential equations are
carefully studied. Linear problems are modelled by partial differential equations
and solved in parallel using PETSc library.
The parallel solution is demonstrated using the wave equation, which is
transformed into the system of ordinary differential equations using the method
of lines.

Solution of nonlinear problems is introduced together with several optimisations
that significantly increase the calculation speed. The improvements are
demonstrated using several numerical examples.

Published

2024

Pages

1–15

Journal

Open Computer Science, vol. 14, no. 1, ISSN 2299-1093

DOI

10.1515/comp-2024-0005

UT WoS

001270179500001

EID Scopus

2-s2.0-85198900421

BibTeX

@article{BUT188923,
  author="Petr {Veigend} and Gabriela {Nečasová} and Václav {Šátek}",
  title="Solving linear and nonlinear problems using Taylor Series Method",
  journal="Open Computer Science",
  year="2024",
  volume="14",
  number="1",
  pages="1--15",
  doi="10.1515/comp-2024-0005",
  issn="2299-1093",
  url="https://www.degruyter.com/document/doi/10.1515/comp-2024-0005/html"
}