ReactionPDETerm

ReactionPDETerm[vars,a]

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

ReactionPDETerm[{u,{x1,…,xn}},a,pars]

uses model parameters pars.

Details

  • Reaction terms are used to model absorption or emission in a number of domains, such as biology, chemistry and physics.
  • Reaction with a reaction coefficient is the process of absorbing of the dependent variable :
  • ReactionPDETerm returns differential operators term to be used as a part of partial differential equations:
  • ReactionPDETerm can be used to model reaction 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 reaction term in context with other PDE terms is given by:
  • The reaction coefficient has the following form:
  • scalar a
  • For a system of PDEs with dependent variables {u1,…,um}, the reaction represents:
  • The reaction term in context systems of PDE terms:
  • The reaction coefficient is a tensor of rank 2 of the form where each submatrix is a scalar that can specified in the same way as for a single dependent variable.
  • The reaction 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

open allclose all

Basic Examples  (4)

Define a stationary reaction term:

Define a stationary reaction term with a parameter:

Solve a reaction diffusion equation build with basic terms:

Visualize the result:

Solve for the eigenvalues of a reaction diffusion equation:

Scope  (6)

Define a time-dependent reaction term:

Define a symbolic reaction term:

Define a 2D stationary reaction term:

Define a reaction term with multiple dependent variables:

Define a Helmholtz model:

Solve for the eigenvalues of the Helmholtz equation:

Solve the Helmholtz equation with a source term:

Visualize the solution:

Solve a nonlinear reaction diffusion equation build with basic terms:

Visualize the result:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2024_reactionpdeterm, author="Wolfram Research", title="{ReactionPDETerm}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/ReactionPDETerm.html}", note=[Accessed: 21-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_reactionpdeterm, organization={Wolfram Research}, title={ReactionPDETerm}, year={2020}, url={https://reference.wolfram.com/language/ref/ReactionPDETerm.html}, note=[Accessed: 21-November-2024 ]}