DerivativePDETerm
DerivativePDETerm[vars,γ]
represents a load derivative term 
with load derivative coefficient 
and model variables vars.
DerivativePDETerm[vars,γ,pars]
uses model parameters pars.
Details
- A load derivative is typically used to model derivatives of a source or sink.
- Computing a derivative with a source derivative coefficient
is the process of adding the derivative of a source in a model by: - DerivativePDETerm returns a differential operators term to be used as a part of partial differential equations:
- DerivativePDETerm can be used to model derivatives 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 derivative term
in context with other PDE terms is given by: - The coefficient
affects the meaning of NeumannValue. - The source derivative coefficient
has the following form: -
{γ1,…,γn} 
vector 
- For a system of PDEs with dependent variables {u1,…,um}, the load derivative represents:
- The derivative term in context systems of PDE terms:
- The load derivative coefficient
is a tensor of rank 3 of the form 
where each subvector 
is a vector of length 
that is specified in the same way as for a single dependent variable. - The load derivative coefficient
can depend on time, space, parameters and the dependent variables. - The following parameters pars can be given:
-
parameter default symbol "RegionSymmetry" None 
- 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 
- All quantities that do not explicitly depend on the independent variables given are taken to have zero partial derivative.
Examples
open allclose allBasic Examples (3)
Define a time-independent derivative term:
Activate the derivative term:
Define a time-dependent derivative term:
Solve a diffusion equation with a nonlinear derivative term and a source term:
Scope (9)
Define a symbolic derivative term:
Define a 1D axisymmetric time-independent derivative term:
Apply Activate to the term:
Verify that the axisymmetric case is a consequence of using a truncated cylindrical coordinate system using the operators that compose the derivative term:
Define a 2D stationary derivative term:
Define a 2D axisymmetric time-independent derivative term:
Apply Activate to the term:
Verify that the axisymmetric case is a consequence of using a truncated cylindrical coordinate system using the operators that compose the derivative term:
Define a derivative with multiple dependent variables:
Define a nonlinear derivative with multiple dependent variables:
Define a nonlinear 2D axisymmetric derivative with multiple dependent variables:
The DerivativePDETerm can be used to compute the derivative of a differential equation component. Set up variables, a region and a boundary condition:
Set up a term for which the derivative is needed in the differential equation:
Solve the equation while explicitly computing the derivative of the term:
Show that the solutions are identical up to numerical precision:
Set up a system of derivative terms with DerivativePDETerm:
Text
Wolfram Research (2020), DerivativePDETerm, Wolfram Language function, https://reference.wolfram.com/language/ref/DerivativePDETerm.html.
CMS
Wolfram Language. 2020. "DerivativePDETerm." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DerivativePDETerm.html.
APA
Wolfram Language. (2020). DerivativePDETerm. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DerivativePDETerm.html