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Disclaimer: I am not really certain if this belongs here, or on the meta site or nowhere. I want to explain though, that I was motivated by the discussion regarding whether or nor we can improve the quality of posts with tag differential-equations.

Hope: I am hoping that this might be a useful thread for all users -perhaps more relevant to new users or more experienced people with Mathematica but not so with PDEs- where we can very broadly discuss the general aspects regarding the new features and updates on PDEs. Perhaps, this thread might be the go-to place before someone decides to write and post a new question.

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In May of 2021, the new version of Mathematica; v 12.3 has a lot of nice, nifty new features, but perhaps what gets me most excited are the new updates pertaining to Differential Equations. More specifically, we see that we have PDE modeling operators as well as the new symbolic solutions of PDEs.

If the moderators give the green light to this and is not closed as off-topic, perhaps we can start adding more thorough answers, and I can add some examples as I play a bit around and experiment.

It goes without saying, that if there are 3 or 4 comments suggesting that this should be closed, I am happy to delete it.

Comment: in case that this turns out to be useful, maybe there could be some sort of pinned link or something like that to make it easy to review the basics before asking.

Final comment: in case that the scope is not clear, please let me know and I will try to elaborate further.

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    Would this be better for Meta maybe? That said, I want 12.3 like a vengeance! May 17 at 20:58
  • Not quite sure to be honest, and this is why I started with that particular disclaimer. I am not very familiar with the topics on the Meta, and this is why I did not post it there directly. May 17 at 21:00
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    @DiSp0sablE_H3r0 Thank you very much for this post. I forgot that I paid for update. Also we can discus some new function of v. 12.3 in this post. May 17 at 21:21
  • @AlexTrounev I had forgotten about it as well, but I received an email an hour or so ago, and started looking at the new features. Quite excited for the new version to be honest! May 17 at 21:24
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    Perhaps a better forum for this would be the Wolfram Community site. May 17 at 22:44
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    DiSp0sablE_H3r0, can you please clarify if you have access to the new update? I haven’t heard a word yet, and I also pay for updates, AND I’m impatient! May 18 at 3:15
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    @CATrevillian It's now available on Wolfram Cloud :) .
    – xzczd
    May 18 at 3:16
  • @CATrevillian I don't have access yet. No May 18 at 5:39
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For PDE's and ODE's, these are the results I have, updated for Version 12.3.

For Kamke test suite (1940 ODE') and for my own PDE test suite (2000 PDE's).

enter image description here

And for PDE's

enter image description here

DSolve has improved for both solving ODE's and PDE's in 12.3, but the improvement in ODE's is much more than for PDE's in these test.

As far as the timing performance itself, I really did not see difference from earlier version (all on same PC). It took about the same time as for the earlier version. May be the speed performance mentioned for 12.3 (compiler, LLVM, etc..) was not yet applied to DSolve code. I do not know.

Update July 25, 2021

For integration, version 12.3.1 scored better by a small amount than 12.1. Here is the table of results over different versions

enter image description here

This table shows the percentage and count of solved and not solved integrals for each version. There are a total of 14,954 integrals in the test suite. The integrals are part of Rubi's input files maintained by Albert Rich.

enter image description here

Here is a bar chart of the above enter image description here

As for timing, there was not much difference in timing between version 12.3.1 and 12.1. All on same PC.

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  • thanks very much for the feedback. I am looking forward to the next one related to integrals May 25 at 7:17

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