Consider the partial differential equation (PDE)
with initial condition and boundary conditions
is the thermal diffusivity. This problem represents the transient heat conduction in a slab. This Demonstration obtains the temperature profile
for user-set values of the dimensionless time
and the thermal diffusivity
. The red curve and the dashed blue curve are obtained using Mathematica
's built-in function NDSolve
and the differential transformation method (DTM), respectively. Here, the DTM gives reasonably good results despite its simplicity.