Heat Eqn. solved with the L-stable Coefficients

The heat equation with a step function as boundary condition for temperature at time t=0 is solved below, following the example from DaFeda's post. The Method of Lines has been incorporated with the Rosenbrock method using the L-stablecoefficients. The step function used a boundary condition of 100 deg F for locations between 0.25 and 0.7 units along the length, at time t=0. The spatial solution is plotted below.