Jump to content

Talk:Relaxation (iterative method)

Page contents not supported in other languages.
From Wikipedia, the free encyclopedia

Over-focused

[edit]

This article over-focuses on the a specific application of the method, needs to be expanded to the entire general concept. —Preceding unsigned comment added by 129.97.58.55 (talkcontribs) 02:24, October 21, 2007 (UTC)

Can you give an example of the relaxation method applied to something else than the numerical solution of an elliptic p.d.e.?  --Lambiam 11:39, 21 October 2007 (UTC)[reply]
Can you give an example of a linear system of equations that does not arise from numerical partial differential equations? The article focus on a specific application in about 60% of the text body, while it does not explain at all what relaxation actually means. — Preceding unsigned comment added by 212.201.70.9 (talk) 21:42, 7 July 2012 (UTC)[reply]

Error term on second-order central difference scheme

[edit]

Shouldn't the error term on the second-order central difference scheme be O(h^2) instead of O(h^4) ? —Preceding unsigned comment added by Runebarnkob (talkcontribs) 10:33, 22 November 2007 (UTC)[reply]

I don't think so. In one dimension
If you do this in two orthogonal directions and add to get as used in the equation for φ(x, y), you still have an error term of O(h4).  --Lambiam 14:21, 22 November 2007 (UTC)[reply]
I agree that the error term should still be the same as you expand the dimension. But I thought that the one dimensional second order three-point central difference scheme was
Maybe I have a lack in my understanding of the BigO-notation. --Runebarnkob (talk) 04:20, 23 November 2007 (UTC)[reply]
That formula is equivalent with
which is clearly too weak; it does not tell us that
Use the Taylor expansion
and the same with h replaced by −h, substituting it for φ(x±h) in the second-order difference formula, and you're done.  --Lambiam 08:51, 23 November 2007 (UTC)[reply]
I agree with you now. I definitely had a problem with my understanding of the O(). Thanks for your patience, Lambiam. --Runebarnkob (talk) 09:55, 23 November 2007 (UTC)[reply]

Shouldn't be in the varphi(x,y), twice the h^2{\nabla}^2\varphi(x,y)\right)? —Preceding unsigned comment added by 89.120.154.196 (talk) 18:30, 30 January 2011 (UTC)[reply]