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Amazing comparison (700+ pages!) of PDE solving. There's a gap to be filled

Posted 5 days ago
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On February 11, Nasser M. Abbasi compiled a huge report about PDE solving with Mathematica 11.3 and a recent (2018 version) of another major CAS system , listing some of the PDE textbooks consulted (strangely no one among Evans, Farlow, Strauss, Sauvigny, Taylor is included).

According to the results and to the table of results , Mathematica is dramaticaly behind its competitor and the knowledge of PDE by both the system seem very limited, compared to results one can find in a textbook.

To be noticed, if you look at his page , Abbasi seems to use more Mathematica than the competitor.

Let's hope that researchers at Wolfram will implement a better knowledge of PDE into Mathematica, rather than spreading their efforts on all those (some of them kind of bizarre) fields : not just to fill the gap with its competitor, but because PDE is a very crucial MATHEMATICAL topic.

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I would venture to say that numeric solving of PDEs is vastly more important than exact solving. I am guessing this comparison is much more about the latter.

Dan, that is all you are able to say??? This report clearly shows, that Mathematica symbolic capabilities for PDE are dramatically poor. Wolfram developers should work very hard on this topic instead of introducing numerous bizare new functionalities.

Posted 4 days ago

Indeed! Though, it's also true that symbolic manipulations (and exact solutions) give the big allure to CASs

Question of NDSolve limitation: are there any major ones? (Neil Singer, AC Kinetics, Inc. gave a great answer as to what is underlying - the underlying components are not hidden they are available to read)

https://community.wolfram.com/groups/-/m/t/1396110?p_p_auth=j28cKFEd

I did not get past the first few of 700 pg. However I saw some inconsistency.

(1) maple cannot do arbitrary precision so it cannot answer "the same questions" mm is

(2) mathematica was counted as "incapable" due to time of solving - which does not mean it cannot solve (it)

(3) in the maple column unsolved integrals were "allowed", but apparently not in mm's column

(from links above, a result mathematica "failed")

DSolve[{cw(1,0)(x,t)+w(0,1)(x,t)=0,w(x,0)=f(x),w(0,t)=h(t)},w(x,t),{x,t},Assumptions->c>0 && x>0 && t>0]

https://www.12000.org/my_notes/pde_in_CAS/pdse4.htm#7

I do not think this test is "correct". c>0 does not mean, in Mathematica, that c is a constant.

"therefore w(x(t),t) is constant" (from link above of test results)

olver intro to PDE, transport and traveling wave equations, "in which c is a fixed, nonzero constant" (which i borrowed from the intro (still saving to afford a copy!))

Correct me if i'm wrong that c>0 does not mean "is a constant" in Mathematica but that in Maple it likely does

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