If you have time and want to learn something useful, use the operator L that
you used in Assignment 3.
Make a copy of your codes from Assignment 3.
Do not work on the original files.
If you have time and want to learn something useful, use the operator L that
you used in Assignment 3.
Make a copy of your codes from Assignment 3.
Do not work on the original files.
If you do not have time, use the heat equation.
Use Matlab if necessary.
You might it useful to do this quickly even if you work with your Assignment 3
codes.
Your domain will be (t,x) = (0,1)2.
The solution u(t,x) is given by
| u(t,x) = (1+t)sin(pi*x). |
Implement the variable weight method with weights theta of 0, .5, 1, and
the special weight of .5-1/(12rho).
Choose rho so that the methods are stable and the error is no more than
10-4.
For each method, determine if you should refine the t or the x mesh spacing
to reduce the cost of getting your result faster.
Since the systems are typically tridiagonal, you can estimate this using the
number of time steps versus the number of spatial points.
Provide full details of what you did.
Finally, make a tar file of your codes from Assignments 3 and 5, uuencode the
tar file, and e-mail it to me.
Then have a nice summer.
Cheers,
Craig C. Douglas
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http://www.ms.uky.edu/~ccd/ma625/a1.html.
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