### 10.2 Simulation of the Diffusion Equation

The following simulation in Fig.10.1 of one-dimensional equilibration or
diffusion process shows for example the time and space dependence of the
temperature after heating a homogeneous thermally insulated thin wire at a
point.

According to the above mentioned special solution an approximated delta function at
the origin is used as initial function, that spreads in Gaussian shape under conservation
of the area under the curve (the amount of heat). The arrows indicate the
$1\u2215e$-width,
the number field the respective point in time. The diffusion constant
$a$ can
be adjusted with the slider over a wide range of values.

The description pages contain further hints.