# Documentation

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# PDE Solvers

Solve elliptic, parabolic, hyperbolic, and eigenvalue problems, or assemble finite element matrices

The toolbox provides two solvers:

• `solvepde` is a general PDE solver for all supported PDE problems, with the exception of eigenvalue problems. This solver returns a `StationaryResults` or `TimeDependentResults` object whose properties contain the solution and its gradient at the mesh nodes.

• `solvepdeeig` is a solver for PDE eigenvalue problems. This solver returns an `EigenResults` object whose properties contain the solution eigenvectors calculated at the mesh nodes.

To assemble finite element matrices that represent the PDE problem, use `assembleFEMatrices`.

## Functions

 `assembleFEMatrices` Assemble finite element matrices `solvepde` Solve PDE specified in a PDEModel `solvepdeeig` Solve PDE eigenvalue problem specified in a PDEModel
 `adaptmesh` Adaptive 2-D mesh generation and PDE solution

## Properties

 PDESolverOptions Properties Algorithm options for PDE solvers

## Topics

### PDE App Workflow

Adjust Solve Parameters in the PDE App

Solve a 2-D PDE problem interactively.

### Concepts

Finite Element Method (FEM) Basics

Description of the use of the finite element method (FEM) to approximate a PDE solution using a piecewise linear function.

Finite Element Basis for 3-D

Description of the use of the Finite Element Method (FEM) for 3-D geometry.

Elliptic Equations

Mathematical definition and discussion of the elliptic equation

Parabolic Equations

Mathematical definition and discussion of the parabolic equation

Hyperbolic Equations

Mathematical definition and discussion of the hyperbolic equation

Eigenvalue Equations

Mathematical definition and discussion of the eigenvalue equation

Nonlinear Equations

Mathematical definition and discussion of nonlinear equations

Systems of PDEs

Mathematical definition and discussion of a system of elliptic equations

References

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