Conference paper

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
Publication language:english
Original title:Numerical Solution of Wave Equation Using Higher Order Methods
Title (cs):Numerické řešení vlnové rovnice metodami vyšších řádů
Pages:1-4
Proceedings:15th International Conference of Numerical Analysis and Applied Mathematics
Conference:15th International Conference of Numerical Analysis and Applied Mathematics
Place:Thessaloniki, GR
Year:2017
URL:https://aip.scitation.org/doi/10.1063/1.5043964
ISBN:978-0-7354-1690-1
DOI:10.1063/1.5043964
Publisher:American Institute of Physics
Keywords
PDE, ODE, Method of Lines, MTSM, difference formulas
Annotation
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.
BibTeX:
@INPROCEEDINGS{
   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 = {http://www.fit.vutbr.cz/research/view_pub.php.en.iso-8859-2?id=11417}
}

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