Publication detail

Solving linear and nonlinear problems using Taylor Series Method

VEIGEND, P. NEČASOVÁ, G. ŠÁTEK, V.

Original Title

Solving linear and nonlinear problems using Taylor Series Method

Type

journal article in Web of Science

Language

English

Original 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.

Keywords

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

Authors

VEIGEND, P.; NEČASOVÁ, G.; ŠÁTEK, V.

Released

12. 7. 2024

ISBN

2299-1093

Periodical

Open Computer Science

Year of study

14

Number

1

State

Federal Republic of Germany

Pages from

1

Pages to

15

Pages count

15

URL

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

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"
}