Solution of the heat problem--Fixed end temperatures

Look at the example in Section 2.3. The following heat problem is solved

   

with solution

   

Here are animations of the solution with parameters a = 1 and k = 1 for the time t = 0 to 1.
On the left is an animation with equally spaced times from t = 0 to 1.
On the right, the animation uses logarithmically spaced times. This makes it easier to see how the solution changes at times near 0.