Talk:Homotopy analysis method

NPOV: this is a highly specialized article not written in an encyclopedic style. It contains references to primary literature only, and all these references share an author. The only external link is to this latter author's personal web site. It is clear that this entry is not objective but rather it is entirely for vanity and promotion of personal interests. 03:11, 25 September 2013 (UTC) — Preceding unsigned comment added by 68.35.11.195 (talk)

Unsigned: This article has been significantly improved by Lin719 and myself. First, theoretical justification of the method has been added. Applications with relevant and diverse articles are now included. The references section has been changed to an in-text system which is now dominated by secondary sources. Finally, much of the overly hyped material has been removed or modified. Though this article can use further improvements (e.g. several more sources, language clarity, a specific worked example from the literature), in my opinion it is now in an encyclopedic form and is sufficiently supported to be removed from being "Stub" class to "Start" class and that the neutrality and primary sources boxes be removed. I will make these category/flag changes in one week if there is no objection. Rememberlands (talk) 21:21, 21 November 2013 (UTC)

I had similar concerns to the unsigned comment from Sept 2013, but the method is widely used and Liao's 2003/2004 papers now have thousands of citations and other researchers extending and applying the method. I do still feel like the article is not quite NPOV - it reads like the abstract or intro of a paper by the originator of the method - in particular, the whole "Characteristics" section basically reads as "this is the best method for reasons A, B, C, much better than all the others, huge breakthrough," as opposed to "this is what the method is useful for, these are its limitations, here's the underlying idea." I think that section in particular should have all its material supported by inline citations from secondary/tertiary sources - otherwise it just sounds like a grant proposal or advertising copy. The rest of the article has some NPOV bits here and there, but not as bad - the second half of the intro, the last paragraph of "Brief Mathematical Overview", and the computer algebra section has only primary sourcing and direct links to the originator's website/code repository.

To be clear, I think the whole article is viable and useful, but does need some editing/rewriting to ensure neutral point of view and sufficient secondary/tertiary sourcing - especially for the soft advocacy of words/phrases like "easily," "simply," "overall [..] useful generalization", "gives the mathematician freedom", "gives excellent flexibility", "greater generality of the method", "naturally show convergence [..] unusual [among] analytic approaches", "distinguishes itself", "simple way to guarantee convergence [..] differentiates HAM". Thank you to various contributors who have worked on this article - the mathematical description in particular looks good; I would make that the centerpiece of the article, because that's what many of the people who come to the page will be looking for. Krb19 (talk) 16:00, 14 May 2019 (UTC)

Language style
The article keeps using the phrase "the HAM" where the definite article is unnecessary. If people agree with this I will remove the definite article. --kupirijo (talk) 11:59, 15 April 2020 (UTC)

First application of homotopy analysis method
The first application of HAM seems to be in a thesis from 1989, it is in nonlinear differential equation system, calculating the electron transport in submicronstures. If this is correct, please insert the reference in the lemma 77.179.170.214 (talk) 22:47, 9 March 2023 (UTC)

The term $$u_m(x)$$ is not defined.
The term $$u_m(x)$$ is not defined. Based on the usual definition of the Taylor series, I suspect it should be $$u_m(x) := \tfrac{1}{m!} \partial_q^m U(q,x)$$. However, given that I'm currently trying to learn the topic from this Wikipedia entry, I don't have the credentials to confirm this and edit the entry. Could anyone else weigh in?