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This question is essentially an applied mathematics version of Which are the best mathematics journals, and what are the differences between them?

Unfortunately, unlike the above question I was not able to find out so far what is the community consensus on top journals in applied mathematics (with statistics excluded -- it is a world of its own), and the question on top specialized journals also leaves the applied mathematics as a whole untouched. The problem is further exacerbated by the fact that while in principle many top generalist math journals declare willingness to publish applied mathematics papers, the fact is that such papers are published there only exceptionally, hence my question.

To make things clear let me reiterate that I would like to understand what is the community consensus (if any) on what are the top applied mathematics journals rather than being shown various numerical rankings (like, say, those based on the impact factor) of which I am quite aware.

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    $\begingroup$ Downvoter(s), would you please comment on how to improve the question? $\endgroup$
    – just-someone
    Commented Nov 8, 2016 at 23:14

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I think there is no equivalent of the Annals for applied math but, in my opinion, some flagships are

  • SIAM Review

  • Mathematics of Computation

  • Foundations of Computational Mathematics

but at least the two latter are not for applied math in general but with a special focus on computation. Moreover, the other SIAM journals are top for their subfields and specific for optimization "Mathematical Programming" is top.

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    $\begingroup$ Thanks! How about Advances in Applied Math? Is it any good? $\endgroup$
    – just-someone
    Commented Nov 9, 2016 at 6:15
  • $\begingroup$ @just-someone: what do you mean by "is it any good"? -- In any case, in spite of the name, the scope of Advances in Applied Mathematics is not limited to applied mathematics. -- For example, I have published there already a pure mathematics paper (see here). $\endgroup$
    – Stefan Kohl ♦
    Commented Nov 9, 2016 at 14:51
  • $\begingroup$ @StefanKohl: Thanks for the comment. I basically wondered whether Adv Appl. Math. has the same (or better) stature within the applied math community as the Advances in Math has in the pure math community. $\endgroup$
    – just-someone
    Commented Nov 9, 2016 at 15:43
  • $\begingroup$ "Mathematical Programming". Oh, what language, FORTRAN? Drum roll, Smitty. An oldie but goodie. (This happened t me in real life.) Seriously, the publishing professional society of "Mathematical Programming", series A, B, and C was founded as the :"Mathematical Programming Society" in 1973, and changed its name to the more understandable by the non-O.R.-inclined "Mathematical Optimization Society" in 2010. However, the journal names have been left as "Mathematical Programming". $\endgroup$
    – Mark L. Stone
    Commented Nov 16, 2016 at 6:20
  • $\begingroup$ Based on my experience in numerical analysis of PDEs, it seems that Foundation of Computational Mathemtics (FoCM) is less known than Mathematics of Computation, Numerische Mathematik, or SIAM journals. Do you think FoCM is at the same level of these journals? $\endgroup$
    – John
    Commented Jun 22, 2019 at 2:04
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I don't think you can have a broad answer to this question. The reason is that there is no generalist applied mathematics journal, that everybody is aiming at. So you only have more focused top journals whithin each subject. Maybe you can aim for a list of those. I can give my very limited contribution with respect to fields adjacent to mine:

For many areas: All SIAM journals.

Optimization:

Mathematical Programming

Mathematics of Operations Research

Numerical Analysis:

IMA Journal of Numerical Analysis

Journal of Computational Physics

Inverse Problems

Mathematics of Computation

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