Question: Animating Boundary Value Problem

Hi everyone,

I'm a student studying pde's and I was trying to find a tool for me to understand it a lot better.

The heat equation is given by: Ut = a^2*Uxx

Take the example of a rod that is insulated at both ends (establishing BC's) of Ux(0,t) = 0 and Ux(L,t) = 0. Let's define the intial condition for any temperature at point x as x*(L-X).  We know that if we try to solve the steady-state solution, setting Ut = 0, we get Uxx = 0 which implies the general solution is U(x) = C1x + C2

From our boundary conditions we can see that a rod insulated at both ends -- and I should say laterally also -- should have a graph that turns from a quadratic to a horizontal line that is defined as the average of the initial conditon function from 0 to L.

In summary: Does maple have a feature to animate the function turning from a quadratic to a horizontal line? I think it would be beneficial in the long term for learning about BC's and visualizing them in my head after I play around with it.