Re: Programming Set 4

[Soroosh Yazdani]

You're supposed to implement four different methods, and you run each
one with different values of h's. So, for example run Euler's method
for h=1/2,1/4,1/8,..,1/1024, and then Modified Euler with
h=1/2,1/4,...,1/1024.

Does that make sense?
Soroosh
On Fri, 2006-12-01 at 23:14 -0800, Meghana Vishvanath wrote:
> Hey Soroosh,
>
> I was wondering about the problem statement for problem 1 on the
> programming set. It says to use four different methods to solve the
> stiff differential equation with different h's and compare the errors.
> If the h's are different in each method, then it doesn't make sense to
> compare the errors (because as h decreases, the error decreases for
> all methods). I don't see how I can make a comparison between
> different h's. Am I misreading the statement?
>
> Thanks,
> Meghana

[Soroosh Yazdani]

Hi Meghana,

I was really hoping someone was going to ask this question at some
point. Yes! There is too much data, and I really don't want to see 60
pages of data.

The short answer to your question is that, you probably want to have a
plot of all of your results on one graph (which will be
indistinguishable from exact value), and few graphs for error analysis.
The error plots, as always, should be log of the absolute value of the
difference. This way, you can really distinguish between how accurate
the results are.

Also, when you are calculating the error, it might be enought to give
out one number that reflects how close two functions are to each other.
Specifically, you should be interested in global truncation error, which
algebraically is defined as max(|y(t_i)-w_i|) for all i in the
appropriate range. If you are making a table of errors, this is the
number that you should print at the end. It is also ok to pick some
random point in the interval and compare the approximate value and the
exact value at that one point, and just print that number out. Either
option gives you certain amount of useful information, and you don't
have to do both (although you should realize what the difference is).

I hope this is helpful. Here is a slightly more general answer to your
question though. These assignments are fairly open ended. The part that
you *have* to do, is to implement some of the algorithms that solve, in
this case, ODE's for you, and then you should assess these to your best
ability and write a report about it. The assessment part means you are
going to play around with these algorithms, and collect lots of data
doing it. By doing this you should be able to get a feel for which
algorithm is best suited for what type of problem. (Usually one is
better than the rest, but maybe not.) Your report should include an
argument on how you came to this conclusion, and present any data that
supports your argument. I think this part of the assignment is the one
that makes programming assignment really difficult, however it can be
very rewarding if your assessment finds something in the data that we've
talked about in class.

Does that make sense?

Soroosh

On Sun, 2006-12-03 at 00:34 -0800, Meghana Vishvanath wrote:
> Hey Soroosh,
>

> I just used those 10 different values for h on the four methods and
> put the t and w values for each of the forty cases and the absolute
> difference between w and the exact value. I used point 7 font and my
> lab report is now 60 pages.
>
> Can I just include the absolute difference to cut the size of this in
> half? Or should I try to make a graph of the errors to more compactly
> represent this (I'm afraid that you won't be able to distinguish the
> numbers because they'll be too small).
>
> Thanks again,
> Meghana
>
> On 12/2/06, Meghana Vishvanath <mvish...@berkeley.edu> wrote:
> Oh, I understand, thanks!
>
>
> On 12/2/06, Soroosh Yazdani <syaz...@math.berkeley.edu>

[zenkalia]

i had that same 60-page problem, so i just compared by absolute error
at t=1, which seemed pretty reasonable since the method has the most
effect on t=1...