Re: math 128
Soroosh Yazdani
so I don't see a definition for local truncation error on page 328,
although they do calculate this error for a general multistep method.
I mentioned what local truncation error for multistep methods is in
section on Wednesday. So, if you look at your notes from there, it might
clarify some of the problems you might be having right now.
Here is a brief explanation: Recall, local truncation error means that
you are assuming that the previous step was exact, and you want to know
how much error you accumulate with one step. Mathematically, assume
w_i=y(t_i) for i=0,1,...,n. The question is what is (y(t_{n+1})-w_{n+1})/h.
Note that in the section, I assumed that you knew the previous 2 or three
values, or however many steps was necessary. I realize now that I might
as well assume that you have the exact first $n$ values.
I've read your next email, however since I'm posting this to the newsgroup
I'm going to make a brief comment that the question is giving you almost
a complete description of a method for approximating an initial value problem
y'=f(t,y). So, you should get used to work with this much detail, and no
more.
Does this answer your question?
Soroosh
On Sun, Nov 19, 2006 at 11:00:22AM -0800, Albert Zhi wrote:
> hi soroosh
> can you give me some idea about even understanding 5.10 #5?
> 1) the professor posted use the definition of location truncation
> error as in page 266. is that a mistake and we should use as in page
> 328 instead? the one on P266 is for one step method only, while the
> problem and P328 are about multiple step method.
> 2) what in the world does the problem want when they ask local
> truncation error? given this method lack of more detail info, it
> looks to me that i can only use the defnition on page 328, with only
> plugging in the coefficients a's and the function F. this will look a
> little too silly so i thought maybe they want something like
> 123/456*h^3*y'''(mu). but how am i gonna get it with so little info?
>
> thank you very much
>
> albert
Albert
but i am still a little unclear of WHY.
i do not yet know why we can get the complete description from just the
approximation, i.e. how am i to know as a priori that i will get all
the info about the error term while the approximation has no info
error, at least not directly.
i know the mechanics to crank the error term, but i kinda wonder that
"philosophically."
it is like, sometimes one may see some nice problem/property and you
can do a lot of math about it, but that person may not understand why,
such as the beautiful topology and geometry underlying the problem,
which determines why things work out well. (like, one can play with
stoke's theorem and crank a lot of stuff out of it, but to really
understand why, one needs to know what working is forms on manifold and
pullback of forms and a bunch of stuff.)
anyway, i was wandering ~, but still wonder.
albert =)
On Nov 20, 9:55 am, Soroosh Yazdani <syazd...@Math.Berkeley.EDU>
wrote: