• #### fyi, couple of report updates

From Nasser M. Abbasi@21:1/5 to All on Wed Dec 23 13:23:11 2020
fyi,

1)
with release of Maple 2020.2 and Mathematica 12.2, I've updated the
"Solving partial differential equations in Maple and Mathematica"
report which uses my collection of PDE's stored in sqlite database,
to see how these systems improved from earlier report which used
Maple 2020 and Mathematica 12.1. All on windows 10, same PC, same
problems.

https://www.12000.org/my_notes/pde_in_CAS/pde_in_cas.htm

Both Maple and Mathematica have improved. With Mathematica going
from solving 72.02% to solving 72.56% of the problems and Maple going
from solving 89.41% to 89.51%.

Total number of PDE's is 2,012.

The break down based on PDE type is also given above in a table.

The current PDE collection is heavily influenced by PDE's from
Handbook of first order partial differential equations by Polyanin, Zaitsev (2004),
(1,585 PDE's added so far) where Maple does better on first order
PDE's.

Mathematica scored better on Hyperbolic PDE's (Wave) and
Parabolic PDE's (Diffusion) while Maple scored a little better
on Elliptic PDE's (Laplace, Poisson, Helmholtz).

Maple is still faster. Using about 9 hrs to solve all problems and Mathematica about 14.5 hrs. There is 10 minutes time-limit on each PDE.

2)
I've updated my own program which generates step-by-step solution of
ODE's.

"Solved dfferential equations problems from selected text books"

https://www.12000.org/my_notes/solving_ODE/index.htm

Now it has 3,647 ODE's solved. These are collection from 25 different textbooks. The program now can solved many types of first order
and second order ODE's and system of linear ode's. And shows
step-by-step solution for each. Ofcourse, there is still some bugs
and improvement needed there. The program verifies each ODE solution
using Maple's odetest. It harder to develop, since it has to generate
Latex at the same time as it runs.

--------------
fyi, I will also be updating the CAS integration test reports at

https://www.12000.org/my_notes/CAS_integration_tests/index.htm

Using the new versions of CAS, which will take about 2 months to complete.

It will use the same Rubi's test suite input files as last time, but with any newer versions of any CAS used before which has been updated and available
at this time.

--Nasser

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