Differential equations, version 12.3 and improving the level of the questions

Question

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.

Answer 1

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).

And for PDE's

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

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.

Here is a bar chart of the above

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