Detail publikačního výsledku

Numerical Solution of Wave Equation Using Higher Order Methods

NEČASOVÁ, G.; KUNOVSKÝ, J.; ŠÁTEK, V.

Originální název

Numerical Solution of Wave Equation Using Higher Order Methods

Anglický název

Numerical Solution of Wave Equation Using Higher Order Methods

Druh

Stať ve sborníku v databázi WoS či Scopus

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

NEČASOVÁ, G.; KUNOVSKÝ, J.; ŠÁTEK, V.

Rok RIV

2019

Vydáno

25.09.2017

Nakladatel

American Institute of Physics

Místo

Thessaloniki

ISBN

978-0-7354-1690-1

Kniha

15th International Conference of Numerical Analysis and Applied Mathematics

Strany od

1

Strany do

4

Strany počet

4

URL

https://aip.scitation.org/doi/10.1063/1.5043964

Plný text v Digitální knihovně

http://hdl.handle.net/

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"
}