equation on a rod
Imagine that you have a rod of length L. It could be considered as a 1D
heat equation problem and we could draw the rod on the x-axis
of the left figure.
The 1D heat equation is in the form
ut = k uxx .
u (x,t) = Temperature (Kelvin)
x = Distance from the left side of the
rod (in meters)
t = Time (in seconds)
k = Conductivity (in meter*meter/second)
u (0,t) = Random temperature between 150 and 350 K
u x (L,t) = 0 (or flux free condition.)
where L = length of the rod (in meters).
u (0,t) = c where c is a constanst.
(Users could choose c by themselves.)
In this program, we set k = 5 m*m/sec & L = 30 m.
How to use the
It is easy! Click on the left figure to choose the values of green
and gray points on the axes. The green point on x-axis is the point on
the rod we use to plot the right figure.) The gray point is the
constanst "c" for our initial condition.
1. You could learn the behaviors of the heat equation which is trying
smooth the graph.
2. Experience with the initial heat "c" which is about, lesser and
bigger than 250 K. What does the term "uxx" of the heat
to do? How does the random boundary condition effect the
(Hint: On average, the random heat is about 250 K.)
(Notes: The program uses the
difference method to solve the equation with dx=L/50
& dt = 0.49*dx*dx/k .)
Atichart Kettapun (Noom)
University of California at Santa
at the MSRI Mathematical Graphics
at Reed College, Portland, in