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NDSolve`FEM`
NDSolve`FEM`

PDESolve

PDESolve[cdata,bcdata,vd,sd,mdata]

solves a PDE based on coefficient data cdata, boundary condition data bcdata, variable data vd, solution data sd and method data mdata to return new solution data.

Details and Options

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

Load the finite element package:

In[1]:=1
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https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-j4klzi

Set up a NumericalRegion:

In[2]:=2
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https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-nx6wf8
Out[2]=2

Set up variable and solution data:

In[3]:=3
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https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-b1fv3m

Initialize the partial differential equation data:

In[4]:=4
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https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-bly9dw
Out[4]=4

Set up the solution of the linear PDE . Initialize the linear coefficients:

In[1]:=1
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-x43tiv
Out[1]=1

Initialize the linear boundary condition data:

In[2]:=2
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-7wkrax
Out[2]=2

Solve the PDE:

In[3]:=3
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-6avfpj

Post-process the PDE:

In[4]:=4
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-lboorj
Out[4]=4

Set up the solution of the nonlinear PDE . Initialize the nonlinear coefficients:

In[1]:=1
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-rne025
Out[1]=1

Initialize nonlinear boundary condition data:

In[2]:=2
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https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-vpnwli
Out[2]=2

Specify an initial guess:

In[3]:=3
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-qig5x3
Out[3]=3

Solve the nonlinear PDE:

In[4]:=4
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-qpgsf1

Post-process the PDE:

In[5]:=5
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-2u143d
Out[5]=5

Options  (8)Common values & functionality for each option

"FindRootOptions"  (5)

Inspect the number of function calls, steps and Jacobian evaluations needed:

In[7]:=7
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-qhsrxl

Specify that PDESolve is to use the default FindRoot root-finding algorithm:

In[1]:=1
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-xpmvd3

Specify that PDESolve is to use the default affine covariant Newton method:

In[1]:=1
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-jhtmvv

Set up PDESolve to not use Broyden updates:

In[1]:=1
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-8oeke5

Set a PrecisionGoal for the default PDESolve FindRoot method:

In[1]:=1
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-qwi99z

"LinearSolver"  (3)

Specify PDESolve to use a direct method for LinearSolve:

In[1]:=1
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-cvsm5d

Specify PDESolve to use a Krylov method for LinearSolve:

In[1]:=1
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-1o6svn

Specify PDESolve to use a customer function for LinearSolve:

In[1]:=1
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-f0hoo9

Properties & Relations  (1)Properties of the function, and connections to other functions

Options given to PDESolve can be given to NDSolve by specifying "PDESolveOptions":

In[11]:=11
✖
https://wolfram.com/xid/0bmo90qj3dh9obgvoec93mq-k61l5x
Wolfram Research (2019), PDESolve, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/PDESolve.html (updated 2020).
✖
Wolfram Research (2019), PDESolve, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/PDESolve.html (updated 2020).

Text

Wolfram Research (2019), PDESolve, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/PDESolve.html (updated 2020).

✖
Wolfram Research (2019), PDESolve, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/PDESolve.html (updated 2020).

CMS

Wolfram Language. 2019. "PDESolve." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/FEMDocumentation/ref/PDESolve.html.

✖
Wolfram Language. 2019. "PDESolve." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/FEMDocumentation/ref/PDESolve.html.

APA

Wolfram Language. (2019). PDESolve. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/FEMDocumentation/ref/PDESolve.html

✖
Wolfram Language. (2019). PDESolve. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/FEMDocumentation/ref/PDESolve.html

BibTeX

@misc{reference.wolfram_2025_pdesolve, author="Wolfram Research", title="{PDESolve}", year="2020", howpublished="\url{https://reference.wolfram.com/language/FEMDocumentation/ref/PDESolve.html}", note=[Accessed: 31-March-2025 ]}

✖
@misc{reference.wolfram_2025_pdesolve, author="Wolfram Research", title="{PDESolve}", year="2020", howpublished="\url{https://reference.wolfram.com/language/FEMDocumentation/ref/PDESolve.html}", note=[Accessed: 31-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_pdesolve, organization={Wolfram Research}, title={PDESolve}, year={2020}, url={https://reference.wolfram.com/language/FEMDocumentation/ref/PDESolve.html}, note=[Accessed: 31-March-2025 ]}

✖
@online{reference.wolfram_2025_pdesolve, organization={Wolfram Research}, title={PDESolve}, year={2020}, url={https://reference.wolfram.com/language/FEMDocumentation/ref/PDESolve.html}, note=[Accessed: 31-March-2025 ]}