# WavePDEComponent

WavePDEComponent[vars,pars]

yields a wave equation PDE term with model variables vars and model parameters pars.

# Details

• WavePDEComponent returns a sum of differential operators to be used as a part of partial differential equations
• WavePDEComponent can be used to model wave equations with dependent variable , independent variables and time variable .
• Time-dependent model variables vars are vars={u[t,x1,,xn],t,{x1,,xn}}.
• The WavePDEComponent is based on a diffusion term:
• The wave PDE term is realized as a DiffusionPDETerm with as a diffusion coefficient, for a constant resulting in .
• The following model parameters pars can be given:
•  parameter default symbol "WaveCoefficient" 1 "RegionSymmetry" None
• The source term coefficient is a scalar.
• The source term coefficient cannot depend on space.
• A possible choice for the parameter "RegionSymmetry" is "Axisymmetric".
• "Axisymmetric" region symmetry represents a truncated cylindrical coordinate system where the cylindrical coordinates are reduced by removing the angle variable as follows:
•  dimension reduction equation 1D 2D
• If the WavePDEComponent depends on parameters that are specified in the association pars as ,keypi,pivi,, the parameters are replaced with .

# Examples

open allclose all

## Basic Examples(3)

Define a wave PDE component:

Activate the component:

Define a wave PDE component with a symbolic coefficient:

Find the eigenvalues of a wave equation:

## Scope(1)

Define a 2D axisymmetric wave PDE component:

Activate the term:

Wolfram Research (2020), WavePDEComponent, Wolfram Language function, https://reference.wolfram.com/language/ref/WavePDEComponent.html (updated 2022).

#### Text

Wolfram Research (2020), WavePDEComponent, Wolfram Language function, https://reference.wolfram.com/language/ref/WavePDEComponent.html (updated 2022).

#### CMS

Wolfram Language. 2020. "WavePDEComponent." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/WavePDEComponent.html.

#### APA

Wolfram Language. (2020). WavePDEComponent. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WavePDEComponent.html

#### BibTeX

@misc{reference.wolfram_2024_wavepdecomponent, author="Wolfram Research", title="{WavePDEComponent}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/WavePDEComponent.html}", note=[Accessed: 09-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_wavepdecomponent, organization={Wolfram Research}, title={WavePDEComponent}, year={2022}, url={https://reference.wolfram.com/language/ref/WavePDEComponent.html}, note=[Accessed: 09-September-2024 ]}