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:
-
"FindRootOptions" Automatic specify options for FindRoot "LinearSolver" Automatic specify a linear solver and options for it - 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 allclose 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:
Set up the solution of the nonlinear PDE 
. Initialize the nonlinear coefficients:
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":
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