Talk:Finite difference

message: The recurrence equation in description of the Backward difference is incorrect. Looks like the recurrence relation of forward difference has been restated again. 
Backward difference recurrence equation should be Y(x) - Y(x-1)....
:I'm afraid I have no idea what you mean. The right-hand side of the recurrence relation for backward differences is at time n+1, and the rhs for forward difference is at time n. There is no Y defined in the article. -- Jitse Niesen (talk) 05:39, 10 April 2006 (UTC)
thread_title:  Implicit Method (backward difference) 

message: I'm proposing a reorganization of this article and finite difference schemes on Talk:Finite difference schemes. Please comment. -- Jitse Niesen (talk) 11:52, 31 July 2006 (UTC)
thread_title:  Reorganization 

message: What does the symbol "h" refer to in the formulae in this article? I can't find it defined in the article itself. It would be nice if it were clarified.  Showeropera (talk) 18:05, 1 May 2020 (UTC)
thread_title:  Symbol definitions 

message: i am citing this from the article:
"The main problem with the central difference method, however, is that oscillating functions can yield zero derivative. If h(nh)=1 for n uneven, and h(nh)=2 for n even, then f'(nh)=0 if it is calculated with the central difference scheme. This is particularly troublesome if the domain of f is discrete."
can someone clarify this (messy) example? bad expression prevents me from checking if the statement is true. also the statement suggests, that there are no such problems when using the one-sided difference. i'd like to see an example that's problematic with one but not the other, also i'm interested to know how a discrete domain of a (not-yet-discretized) function is reasonable in a case where one wants to approximate the derivative. 91.15.153.48 (talk) 13:45, 16 May 2010 (UTC)
thread_title:  central difference 

message: When it is first presented, the derivative of the univariate "f" is described as "f' = (f(x+h/2) - f(x-h/2))/h".
In the multivariate example, it appears as "f_{x} = (f(x+h,y) - f(x-h,y))/2h" (someone compesates the "h" by dividing by "2h", seems ok...).
However, for the formula of "f_{xx}" it is divided by "h^2". It seems to me that the "h" used for "f_{x}" is not the same as for "f_{xx}". The denominator for "f_{xx}" should be "4h^2" if "f_{xx}" was derived from "f_{x}" (as it seems from the context...). 
I am not a math person... and I may be even wrong... but I've got confused with that... 
Capagot (talk) 19:15, 17 September 2010 (UTC)
thread_title:  Multivariate example 

message: I think it would be welcome to add some info on how these formulas are affected by floating point aritmetics, e.g. the effects of cancellation and the tradeoff between truncation error and rounding error for different step-sizes.  — Preceding unsigned comment added by 130.237.43.79 (talk) 14:04, 11 July 2011 (UTC)
thread_title:  Accuracy 

message: Shouldn't the canonical first few numbers (0, 1, 1, 2...) be used in the Fibonacci example, and not (2, 2, 4) as currently done? Syd Barrett (talk) 21:49, 12 May 2013 (UTC)
thread_title:  Example using the Fibonacci Sequence 

message: Starting with the definition, which appears hard to source as-is. The topic that can actually be found in numerous books is finite difference approximation (of derivatives). The word "approximation" is not gratuitous, because a (first-order) finite difference approximation of the derivative is indeed the difference quotient, and the symmetric difference quotient is the 2nd-order approximation of the (first) derivative etc. See    for instance. ¶ Going to the 1st section of this page, perhaps there are some sources [though none are cited inline on the page] which define the forward/backward/central different without division by h (or 2h), but those I've looked at [see links in previous sentence] don't do that. Also, this article is inconsistent with itself when it moves on to "2nd order central" [section] and so forth, where it defines them as including division by h2 [in the case of the "2nd order central"] etc. Speaking of which, the  "2nd order central" is actually the difference quotient of the second symmetric derivative etc. ¶ So basically Wikipedia has two rather bad quality pages (this and difference quotient) on (more or less) the same topic [framed poorly] an no page on the real topic...  There's a bit better material at numerical differentiation, on the basics at least, but it's not broad enough. Some1Redirects4You (talk) 12:47, 27 April 2015 (UTC)
replies: text: I am not convinced you have not misunderstood WP editorship. This is not a forum of critical discussion, but a hands-on proposed improvements venue. What, exactly, are you proposing to do to improve the article? "Unfunded mandates", asking someone else to fix this to your satisfaction are hardly constructive. I would disagree with you that this is an "off subject" article. It is distinctly not about finite differences as an approximation tool, and more pitched to umbral concepts and techniques. The introduction you are fussing about appears like a bag of definitions for the reader unfamiliar with the language. Why don't you try to rewrite difference quotient to the satisfaction of its editors, instead? Cuzkatzimhut (talk) 13:28, 27 April 2015 (UTC)
replies: text:  I am talking about this article in the paragraph above. If you reread what I wrote carefully, you might see that. Some1Redirects4You (talk) 13:31, 27 April 2015 (UTC)

text: After looking a bit at the various references, it seems the presentation here bears some resemblance to the 1939 book of hu:Jordán Károly. Alas, that's a rather obscure book nowadays, which doesn't seem to have inspired treatment along that line in [m]any subsequent sources. Don't even get me started on the 1870 book of Boole being used as source here. Boole didn't even understand well enough the algebra that bears his name in order to use it a source for contemporary presentations, so I doubt this other books of his is much better. The calculus of finite differences (as conceived/presented in the works of Boole and Károly) doesn't seem to have much relevance today. So it should not influence the presentation outsider of that section, which might even be better to spin off to its own article owing to too numerous idiosyncrasies of little relevance except to math historians, perhaps. Some1Redirects4You (talk) 13:29, 27 April 2015 (UTC)
thread_title:  This page appears to be a bit [[WP:OR]]-framed/misguided and inconsistent (with itself) 

message: User:TonyTheTiger reinserted a gratuitous, indeed, highly inappropriate template on Isaac Newton at the bottom of the article, which I had removed, purporting not to be convinced by my explanation that the article is not a shrine to Newton.
Well, it isn't! Newton's interpolation formula is properly showcased in its own section, but this technical article is not about Newton. George Boole has much more to do with it, or the umbral mathematicians mentioned---and besides, this is not a history-heavy venue. 
Sticking in handles on irrelevant hero-worhip information degrades the quality of the article. The same knee-jerk abuse has been inflicted on Table of Newtonian series , Newton polynomial, etc... It looks like anything with Newton's name in it has been contaminated this way.  I fear the inserter may well  not care to read and understand the article in the first place.  I leave it to somebody else to remove it this time, but ... Behold!  Cuzkatzimhut (talk) 10:35, 15 October 2015 (UTC)
thread_title: Gratuitous distracting Isaac Newton template

message: Here is 
The relationship of these higher-order differences with the respective derivatives is  straightforward,
:\frac{d^n f}{d x^n}(x) = \frac{\Delta_h^n[f](x)}{h^n}+O(h) = \frac{\nabla_h^n[f](x)}{h^n}+O(h) = \frac{\delta_h^n[f](x)}{h^n} + O(h^2).
Since the 
\frac{\Delta_h[f](x)}{h}=\frac{d f}{d x}(x)+O(h)\rightarrow \frac{d f}{d x}(x)<\frac{\Delta_h[f](x)}{h}, so in the expression \frac{d^n f}{d x^n}(x) = \frac{\Delta_h^n[f](x)}{h^n}+O(h) = \frac{\nabla_h^n[f](x)}{h^n}+O(h) = \frac{\delta_h^n[f](x)}{h^n} + O(h^2). the plus symbol should be replaced to minus, or derivative and differnce operators places to be changed inversible.  (Just my oppinion, could be wrong) --KolosovP (talk) 18:23, 4 August 2016 (UTC)
replies: text: You appear confused about the meaning of the Big O notation. This item should have been placed at the bottom of the page as per talk page instructions.Cuzkatzimhut (talk) 16:11, 16 August 2016 (UTC)

text: Wrong.  The definition explicitly emphasizes absolute values, not signs. Please read the article and its illustrations. Cuzkatzimhut (talk) 11:26, 17 August 2016 (UTC)

text: Even that, the aboslute value of derivative taken by some set lesser then abs of differnece, so big O could be negative value ? --KolosovP (talk) 14:26, 17 August 2016 (UTC)
replies: text:  Moved to bottom of the Talk page as per WP rules
What is being bounded is the differences \frac{d^n f}{d x^n}(x) - \frac{\Delta_h^n[f](x)}{h^n}, etc, so no signage is meaningful. Cuzkatzimhut (talk) 16:06, 17 August 2016 (UTC)
thread_title: Possible Mistake

message: Hello fellow Wikipedians,
I have just modified one external link on Finite difference. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
*Added archive https://web.archive.org/web/20090419132601/http://www.stanford.edu:80/~dgleich/publications/finite-calculus.pdf to http://www.stanford.edu/~dgleich/publications/finite-calculus.pdf
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
Cheers.—InternetArchiveBot (Report bug) 19:56, 31 December 2016 (UTC)
thread_title:  External links modified 

message: In the section "Newton's series", in the last formula, at the leftmost summation sign, should not an upper summation bound be mentioned there? I suspect an infinity sign is missing. Is that correct?Redav (talk) 08:40, 17 May 2020 (UTC)
thread_title:  Upper summation limit missing? 

message: In the article I read: "However, the central (also called centered) difference yields a more accurate approximation."
In my view, and as explained after the cited text, given a certain mesh size h, a central difference is not necessarily more accurate than a forward or backward difference.
What seems true is that the rate of convergence to the actual derivative in the limit for small h is faster.
The confusion seems to be as if a higher convergence rate were synonymous with higher accuracy for a fixed value of h. Does anyone disagree?Redav (talk) 10:32, 24 May 2020 (UTC)
thread_title:  More accurate? Or rather of higher order in h? 

message: There seems to be missing denominator h terms in the higher order derivative section. It would be nice to have a citation here to look it up, but I'd guess it is h^n. 018 (talk) 23:44, 12 November 2023 (UTC)
thread_title:  inconsistency in higher order section