FEMDocumentation`
FEMDocumentation`

# 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.

# Examples

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## Basic Examples(3)

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":

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).

#### 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_2022_pdesolve, author="Wolfram Research", title="{PDESolve}", year="2020", howpublished="\url{https://reference.wolfram.com/language/FEMDocumentation/ref/PDESolve.html}", note=[Accessed: 08-June-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_pdesolve, organization={Wolfram Research}, title={PDESolve}, year={2020}, url={https://reference.wolfram.com/language/FEMDocumentation/ref/PDESolve.html}, note=[Accessed: 08-June-2023 ]}