Mathematics |

**Evaluating the Solution at Specific Points**

After obtaining and plotting the solution above, you might be interested in a solution profile for a particular value of `t`

, or the time changes of the solution at a particular point `x`

. The `k`

th column `u(:,k)`

(of the solution extracted in step 7) contains the time history of the solution at `x(k)`

. The `j`

th row `u(j,:)`

contains the solution profile at `t(j)`

.

Using the vectors `x`

and `u(j,:)`

, and the helper function `pdeval`

, you can evaluate the solution `u`

and its derivative at any set of points `xout`

The example `pdex3`

uses `pdeval`

to evaluate the derivative of the solution at `xout = 0`

. See `pdeval`

for details.

**Changing PDE Integration Properties**

The default integration properties in the MATLAB PDE solver are selected to handle common problems. In some cases, you can improve solver performance by overriding these defaults. You do this by supplying `pdepe`

with one or more property values in an options structure.

Use `odeset`

to create the options structure. Only those options of the underlying ODE solver shown in the following table are available for `pdepe`

. The defaults obtained by leaving off the input argument `options`

are generally satisfactory. Changing ODE Integration Properties tells you how to create the structure and describes the properties.

Properties Category |
Property Name |

Error control |
`RelTol` , `AbsTol` , `NormControl` |

Step-size |
`InitialStep` , `MaxStep` |

Solving PDE Problems | Example: Electrodynamics Problem |

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