This assignment is due Thursday, February 25 in class.
Please e-mail your Matlab script(s) to
This assignment is due Thursday, February 25 in class.
Please e-mail your Matlab script(s) to
Do problem 3.3 in the text.
Consider the heat equation in three dimensions:
| ut = uxx + uyy + uzz, | (x,t) in (0,1)3x(0,tF), |
| u(..., t) = 0, | t > 0, along the spatial boundary, |
| u0 = sin(x pi)sin(y pi)sin(z pi). |
Code the ADI method in problem 3.3 and the LOD method (equation 3.25, page 69).
Choose a small number of spatial points (e.g., 8x8x8, but try a bigger grid if
you can).
Run each procedure to time tF=1.
Plot the solutions.
How many time steps do you need for each method to get a similar, good
solution.
Write a report comparing the solutions and how much each method cost.
Draw some concrete conclusions about which method you would use.
Hints: Do not store dense matrices.
Do not store the solution at all time steps, just the ones you need to compute
with at any time step and the one at the end to plot.
Cheers,
Craig C. Douglas