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Time-dependent PDE solution and derived quantities

A `TimeDependentResults`

object contains the solution of a
PDE and its gradients in a form convenient for plotting and
postprocessing.

A

`TimeDependentResults`

object contains the solution and its gradient calculated at the nodes of the triangular or tetrahedral mesh, generated by`generateMesh`

.Solution values at the nodes appear in the

`NodalSolution`

property.The solution times appear in the

`SolutionTimes`

property.The three components of the gradient of the solution values at the nodes appear in the

`XGradients`

,`YGradients`

, and`ZGradients`

properties.The array dimensions of

`NodalSolution`

,`XGradients`

,`YGradients`

, and`ZGradients`

enable you to extract solution and gradient values for specified time indices, and for the equation indices in a PDE system.

To interpolate the solution or its gradient to a custom grid (for example, specified
by `meshgrid`

), use `interpolateSolution`

or
`evaluateGradient`

.

There are several ways to create a `TimeDependentResults`

object:

Solve a time-dependent problem using the

`solvepde`

function. This function returns a PDE solution as a`TimeDependentResults`

object. This is the recommended approach.Solve a time-dependent problem using the

`parabolic`

or`hyperbolic`

function. Then use the`createPDEResults`

function to obtain a`TimeDependentResults`

object from a PDE solution returned by`parabolic`

or`hyperbolic`

. Note that`parabolic`

and`hyperbolic`

are legacy functions. They are not recommended for solving PDE problems.

`evaluateCGradient` | Evaluate flux of PDE solution |

`evaluateGradient` | Evaluate gradients of PDE solutions at arbitrary points |

`interpolateSolution` | Interpolate PDE solution to arbitrary points |

`interpolateSolution`

| `evaluateGradient`

| `evaluateCGradient`

| `EigenResults`

| `StationaryResults`