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.
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
- PDESolve solves linear and nonlinear stationary partial differential equations.
- PDESolve returns a list that is the solution data .
- The coefficient data cdata is a PDECoefficientData object generated by InitializePDECoefficients .
- The boundary condition data bcdata is a BoundaryConditionData object generated by InitializeBoundaryConditions .
- Variable data vd and solution data sd are corresponding lists of variables and values. Templates for vd and sd may be generated using NDSolve`VariableData and NDSolve`SolutionData , and components may be set using NDSolve`SetSolutionDataComponent .
- The method data mdata is a PDE method data object, such as FEMMethodData , generated through InitializePDEMethodData .
- PDESolve takes the following options:
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- Options given to PDESolve can be given to NDSolve by specifying "PDESolveOptions". »
- Setting the option from NDSolve and related functions is explained in NDSolve Finite Element Options.
Examples
open all close allBasic Examples (3)
Load the finite element package:
Set up a NumericalRegion :
Set up variable and solution data:
Initialize the partial differential equation data:
Set up the solution of the linear PDE . Initialize the linear coefficients:
Initialize the linear boundary condition data:
Solve the PDE:
Post-process the PDE:
Set up the solution of the nonlinear PDE . Initialize the nonlinear coefficients:
Initialize nonlinear boundary condition data:
Specify an initial guess:
Solve the nonlinear PDE:
Post-process the PDE:
Options (8)
"FindRootOptions" (5)
Inspect the number of function calls, steps and Jacobian evaluations needed:
Specify that PDESolve is to use the default FindRoot root-finding algorithm:
Specify that PDESolve is to use the default affine covariant Newton method:
Set up PDESolve to not use Broyden updates:
Set a PrecisionGoal for the default PDESolve FindRoot method:
"LinearSolver" (3)
Specify PDESolve to use a direct method for LinearSolve :
Specify PDESolve to use a Krylov method for LinearSolve :
Specify PDESolve to use a customer function for LinearSolve :
Properties & Relations (1)
Options given to PDESolve can be given to NDSolve by specifying "PDESolveOptions":
Related Guides
Text
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.
APA
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: 17-November-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: 17-November-2025]}