Solution of the heat problem- One end fixed temperature, convection at other end

Look at the example in section 2.6. This heat problem is solved there. The interesting thing is the convection condition at the right side.

   

The solution was found as

   
where the eigenvalues are solutions of the equation
   
For the parameter combination
   
the first five values are:

     2.862772588
     5.760557933
     8.708313831
    11.70267808
    14.73347234


Here are animations of the solution for the time t = 0 to 1 with parameters a = 1, k = 1 and
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.