SourcePDETerm

SourcePDETerm[vars,f]

represents a source term with source coefficient and model variables vars.

SourcePDETerm[vars,f,pars]

uses model parameters pars.

Details

  • Source terms are used in a number of domains such as thermodynamics, acoustics, chemistry, physics and fluid dynamics.
  • A source is typically used to model a source or sink.
  • Adding a source with a source coefficient is the process of inserting or removing energy into a model by:
  • SourcePDETerm returns a differential operators term to be used as a part of partial differential equations:
  • SourcePDETerm can be used to model sources in equations with dependent variable , independent variables and time variable .
  • Stationary model variables vars are vars={u[x1,…,xn],{x1,…,xn}}
  • Time-dependent model variables vars are vars={u[t,x1,…,xn],{x1,…,xn}} or vars={u[t,x1,…,xn],t,{x1,…,xn}}.
  • The source term in context with other PDE terms is given by:
  • The source coefficient has the following form:
  • scalar
  • For a system of PDEs with dependent variables {u1,…,um}, the source represents:
  • The source term in context systems of PDE terms:
  • The source coefficient is a tensor of rank 1 of the form where each value is a scalar that can be specified in the same way as for a single dependent variable.
  • The source coefficient can depend on time, space, parameters and the dependent variables.
  • The coefficient does not affect the meaning of NeumannValue.
  • All quantities that do not explicitly depend on the independent variables given are taken to have zero partial derivative.

Examples

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Basic Examples  (3)

Define a time-independent source term:

Define a time-dependent source term:

Solve a Poisson equation constructed from a diffusion and a source term:

Scope  (6)

Define a symbolic source term:

Define a 2D stationary source term:

Define a source term for multiple dependent variables:

Solve a Poisson equation with a source term:

Compute eigenvalues of a Poisson equation constructed from a diffusion and a source term:

Define a Helmholtz model:

Solve the Helmholtz equation with a source term:

Visualize the solution:

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

Text

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

CMS

Wolfram Language. 2020. "SourcePDETerm." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SourcePDETerm.html.

APA

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

BibTeX

@misc{reference.wolfram_2024_sourcepdeterm, author="Wolfram Research", title="{SourcePDETerm}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/SourcePDETerm.html}", note=[Accessed: 22-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_sourcepdeterm, organization={Wolfram Research}, title={SourcePDETerm}, year={2020}, url={https://reference.wolfram.com/language/ref/SourcePDETerm.html}, note=[Accessed: 22-December-2024 ]}