Parameterized solution of one-dimensional thermal diffusion with a heat source and a moving boundary

The construction of a simple, accurate ODE approximation to a 1D thermal-diffusion PDE is constructed, in a case where both a heat source and a moving boundary are present. The illustrative physical problem chosen is that of thermal diffusion and evaporation of a water drop irradiated by laser light absorbed at 10.6 microns. The ODE representation exhibits the same linear stability restriction when solved by an explicit method as the original PDE. (O.C.)