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Numerical Solution of Wave Equation Using Higher Order Methods

NEČASOVÁ Gabriela, KUNOVSKÝ Jiří and ŠÁTEK Václav. 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, pp. 1-4. ISBN 978-0-7354-1690-1. Available from: https://aip.scitation.org/doi/10.1063/1.5043964
Czech title
Numerické řešení vlnové rovnice metodami vyšších řádů
Type
conference paper
Language
english
Authors
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
Conference
15th International Conference of Numerical Analysis and Applied Mathematics, Thessaloniki, GR
ISBN
978-0-7354-1690-1
Publisher
American Institute of Physics
Place
Thessaloniki, GR
DOI
BibTeX
@INPROCEEDINGS{FITPUB11417,
   author = "Gabriela Ne\v{c}asov\'{a} and Ji\v{r}\'{i} Kunovsk\'{y} and V\'{a}clav \v{S}\'{a}tek",
   title = "Numerical Solution of Wave Equation Using Higher Order Methods",
   pages = "1--4",
   booktitle = "15th International Conference of Numerical Analysis and Applied Mathematics",
   year = 2017,
   location = "Thessaloniki, GR",
   publisher = "American Institute of Physics",
   ISBN = "978-0-7354-1690-1",
   doi = "10.1063/1.5043964",
   language = "english",
   url = "https://www.fit.vut.cz/research/publication/11417"
}
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