Re: Finite Difference Methods

vsgdp wrote:
> Hi,
>
> I am in an undergrad numerical analysis course. Our instructor lectured on
> some material not found in the book. Specifically, he talked about a way to
> check stability of finite differencing schemes by studting how each Fourier
> mode evolves in time. Then you can find an "amplification factor" which can
> tell you when the method is stable.
> Sorry if this is vague, but does it sound familiar to anyone? I would like
> to know the technical name for this process so I can do further research
> about it because I do not really understand at present. Also, if anyone
> knows of any books that cover it, I'd like to know their titles.
>
> Thanks in advance.

I just call that "Fourier stability analysis", but since Fourier
methods are so widely used that is a bit vague on its own and it is
probably sensible to say: "Fourier stability analysis of finite
difference schemes".

This topic is covered in detail, and IMO explained well in the book:

Numerical Solution of Partial Differential Equations
by K. W. Morton, D. F. Mayers
Paperback: 239 pages
Publisher: Cambridge University Press (October 20, 1994)
Language: English
ISBN: 0521429226

Most Uni libraries seem to have several copies of this book.

Hope that helps,
andy


PS: Amazon claims it is out of print - but I'm sure I've seen it on
sale recently, and there are bound to be 2nd hand copies around. It's
certainly available for purchase online in PDF file format. Just Google
for the title.

.

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