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
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"
}
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