Publication Details

Numerical Solution of Wave Equation Using Higher Order Methods

NEČASOVÁ, G.; KUNOVSKÝ, J.; ŠÁTEK, V. Numerical Solution of Wave Equation Using Higher Order Methods. In 15th International Conference of Numerical Analysis and Applied Mathematics. Thessaloniki: American Institute of Physics, 2017. p. 1-4. ISBN: 978-0-7354-1690-1.
Czech title
Numerické řešení vlnové rovnice metodami vyšších řádů
Type
conference paper
Language
English
Authors
Nečasová Gabriela, Ing., Ph.D. (DITS)
Kunovský Jiří, doc. Ing., CSc.
Šátek Václav, Ing., Ph.D. (DITS)
URL
Keywords

PDE, ODE, Method of Lines, MTSM, difference formulas

Abstract

The paper deals with the numerical solution of partial differential equations (PDEs). The one-dimensional wave equation was chosen for experiments; it is solved using Method of Lines (MOL) which transforms the PDE into the system of ordinary differential equations (ODEs). The time domain remains continuous, and the Modern Taylor Series Method (MTSM) is used for solving the system of ODES. On the other hand, the space domain is discretized by higher order finite difference formulas. Higher order difference formulas can be unstable. The necessity of the variable precision arithmetic is discussed in this paper. The seven point difference formula is analysed as an example of higher order difference formulas.

Published
2017
Pages
1–4
Proceedings
15th International Conference of Numerical Analysis and Applied Mathematics
ISBN
978-0-7354-1690-1
Publisher
American Institute of Physics
Place
Thessaloniki
DOI
10.1063/1.5043964
UT WoS
000445105400286
EID Scopus
2-s2.0-85049964608
BibTeX 
@inproceedings{BUT155785,
  author="Gabriela {Nečasová} and Jiří {Kunovský} and Václav {Šátek}",
  title="Numerical Solution of Wave Equation Using Higher Order Methods",
  booktitle="15th International Conference of Numerical Analysis and Applied Mathematics",
  year="2017",
  pages="1--4",
  publisher="American Institute of Physics",
  address="Thessaloniki",
  doi="10.1063/1.5043964",
  isbn="978-0-7354-1690-1",
  url="https://aip.scitation.org/doi/10.1063/1.5043964"
}
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