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 1e-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.

Figure 10.1: Animated solution of the diffusion equation with the delta impulse for t = 0 at x = 0. The picture shows the state at t = 2. The arrow indicates the width, where the function has decayed to 1e of the maximum

The description pages contain further hints.