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z.zeng September 14, 2000 22:41

High-order scheme and grid
I am coding a Linear Stability Analysis for fluid dynamic problem, and therefore a genernalized eigenvale problem A x=lamda B x must be solved. The dimension of A and B is (4xNJxNK)^2.(NJ and NK is number of grid in y and z direction). Due to the limitaion of memory, NJxNK can only be up to 30x30, but it seems too coarse for my calcutation.

My quesation is

(1) If a higher-order difference scheme (e.g. 4-order)is adopted in stead of my present 2-order scheme, the problem caused by coarse grid can be remedied?

(2) I remeber that a paper mentioned that a non-homgious grid would reduce the accurate of high-order scheme. I read it several years ago, and can not find it again now. What is your suggestion on a homgious or non-homgious grid?

(3) Could you suggests a good high order difference scheme to me with corresponding literature?

Your advises and suggestions on any above questions are highly appreciated.

Thanks in advance.


frederic felten September 15, 2000 18:05

Re: High-order scheme and grid

Check out the following publication:


Frederic Felten

Chidu September 16, 2000 06:48

Re: High-order scheme and grid

It is a good idea to use a spectral type discretization if you are really limited by a coarse grid. This will give you much better results if your focus is to obtain very accurate eigenvalues.

With finite-difference you can use arbitrarily higher-order approximations which is obviously limited by the number of grid points you have. There is a paper in the SIAM Journal which gives an algorithm to generate coefficients for arbitrary order of accuracy finite-difference scheme. The author escapes my memory, I will look it up and repost.


Z.Zeng September 17, 2000 20:32

Re: High-order scheme and grid
Thanks you all for your kind help.

Chidu mentioned paper seems very interesting, we wish you can find it.


K.S.Ravichandran September 18, 2000 06:25

Re: High-order scheme and grid
Chidu & Zeng

You may look up Fornberg's paper "Generation of Finite-Difference Formulas on arbitrarily spaced grids", Math. Comp. V51, N0184, p699, 1988


Chidu September 18, 2000 10:12

Re: High-order scheme and grid
Exactly, Ravi. This is the paper. I was on vacation and did not have access to the info. Thanks.

regards, chidu...

ajay singh October 14, 2000 13:10

Re: High-order scheme and grid
please guide me for using higher order scheme for les

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