Publication Details

Solving linear and nonlinear problems using Taylor Series Method

VEIGEND Petr, NEČASOVÁ Gabriela and ŠÁTEK Václav. Solving linear and nonlinear problems using Taylor Series Method. Open Computer Science, vol. 14, no. 1, 2024, pp. 1-15. ISSN 2299-1093. Available from: https://www.degruyter.com/document/doi/10.1515/comp-2024-0005/html
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 FIT BUT)
Nečasová Gabriela, Ing., Ph.D. (DITS FIT BUT)
Šátek Václav, Ing., Ph.D. (DITS FIT BUT)
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
Publisher
Walter de Gruyter
DOI
10.1515/comp-2024-0005
UT WoS
001270179500001
EID Scopus
2-s2.0-85198900421
BibTeX 
@ARTICLE{FITPUB13133,
   author = "Petr Veigend and Gabriela Ne\v{c}asov\'{a} and V\'{a}clav \v{S}\'{a}tek",
   title = "Solving linear and nonlinear problems using Taylor Series Method",
   pages = "1--15",
   journal = "Open Computer Science",
   volume = 14,
   number = 1,
   year = 2024,
   ISSN = "2299-1093",
   doi = "10.1515/comp-2024-0005",
   language = "english",
   url = "https://www.fit.vut.cz/research/publication/13133"
}
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