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To specify parameters for solving a PDE, select **Parameters** from the
**Solve** menu. The set of solve parameters differs depending on
the type of PDE. After you adjust the parameters, solve the PDE by selecting
**Solve PDE** from the **Solve** menu or
by clicking the button.

By default, no specific solve parameters are used, and the elliptic
PDEs are solved using the basic elliptic solver `assempde`

.
Optionally, the adaptive mesh generator and solver `adaptmesh`

can
be used. For the adaptive mode, the following parameters are available:

**Adaptive mode**. Toggle the adaptive mode on/off.**Maximum number of triangles**. The maximum number of new triangles allowed (can be set to`Inf`

). A default value is calculated based on the current mesh.**Maximum number of refinements**. The maximum number of successive refinements attempted.**Triangle selection method**. There are two triangle selection methods, described below. You can also supply your own function.**Worst triangles**. This method picks all triangles that are worse than a fraction of the value of the worst triangle (default: 0.5).**Relative tolerance**. This method picks triangles using a relative tolerance criterion (default: 1E-3).**User-defined function**. Enter the name of a user-defined triangle selection method. See Poisson's Equation with Point Source and Adaptive Mesh Refinement for an example of a user-defined triangle selection method.

**Function parameter**. The function parameter allows fine-tuning of the triangle selection methods. For the worst triangle method (`pdeadworst`

), it is the fraction of the worst value that is used to determine which triangles to refine. For the relative tolerance method, it is a tolerance parameter that controls how well the solution fits the PDE.**Refinement method**. Can be`regular`

or`longest`

. See Specify Mesh Parameters in the PDE Modeler App.

If the problem is nonlinear, i.e., parameters in the PDE are
directly dependent on the solution `u`

, a nonlinear
solver must be used. The following parameters are used:

**Use nonlinear solver**. Toggle the nonlinear solver on/off.**Nonlinear tolerance**. Tolerance parameter for the nonlinear solver.**Initial solution**. An initial guess. Can be a constant or a function of*x*and*y*given as a MATLAB^{®}expression that can be evaluated on the nodes of the current mesh.Examples:

`1`

, and`exp(x.*y)`

. Optional parameter, defaults to zero.**Jacobian**. Jacobian approximation method:`fixed`

(the default), a fixed point iteration,`lumped`

, a “lumped” (diagonal) approximation, or`full`

, the full Jacobian.**Norm**. The type of norm used for computing the residual. Enter as`energy`

for an energy norm, or as a real scalar*p*to give the*l*p norm. The default is`Inf`

, the infinity (maximum) norm.### Note

The adaptive mode and the nonlinear solver can be used together.

The solve parameters for the parabolic PDEs are:

**Time**. A MATLAB vector of times at which a solution to the parabolic PDE should be generated. The relevant time span is dependent on the dynamics of the problem.Examples:

`0:10`

, and`logspace(-2,0,20)`

**u(t0)**. The initial value*u*(*t*_{0}) for the parabolic PDE problem The initial value can be a constant or a column vector of values on the nodes of the current mesh.**Relative tolerance**. Relative tolerance parameter for the ODE solver that is used for solving the time-dependent part of the parabolic PDE problem.**Absolute tolerance**. Absolute tolerance parameter for the ODE solver that is used for solving the time-dependent part of the parabolic PDE problem.

The solve parameters for the hyperbolic PDEs are:

**Time**. A MATLAB vector of times at which a solution to the hyperbolic PDE should be generated. The relevant time span is dependent on the dynamics of the problem.Examples:

`0:10`

, and`logspace(-2,0,20)`

.**u(t0)**. The initial value*u*(*t*_{0}) for the hyperbolic PDE problem. The initial value can be a constant or a column vector of values on the nodes of the current mesh.**u'(t0)**. The initial value $$\dot{u}$$(*t*_{0}) for the hyperbolic PDE problem. You can use the same formats as for**u(t0)**.**Relative tolerance**. Relative tolerance parameter for the ODE solver that is used for solving the time-dependent part of the hyperbolic PDE problem.**Absolute tolerance**. Absolute tolerance parameter for the ODE solver that is used for solving the time-dependent part of the hyperbolic PDE problem.

For the eigenvalue PDE, the only solve parameter is the **Eigenvalue
search range**, a two-element vector, defining an interval
on the real axis as a search range for the eigenvalues. The left side
can be `-Inf`

.

Examples: `[0 100]`

, `[-Inf 50]`

Before solving a nonlinear elliptic PDE in the PDE Modeler app, select
**Solve****Parameters**. Then select
**Use nonlinear solver** and click
**OK**.