FYI,
The following is a new report showing results of running
a large collection of ODE's using Maple and Mathematica
and comparing their performance
https://www.12000.org/my_notes/CAS_ode_tests/index.htm
On Monday, April 18, 2022 at 6:22:32 AM UTC-4, Nasser M. Abbasi wrote:
FYI,
The following is a new report showing results of running
a large collection of ODE's using Maple and Mathematica
and comparing their performance
https://www.12000.org/my_notes/CAS_ode_tests/index.htm
Why does you table have Mathemetica placed in the row above that in which Maple is placed?
In several (almost all?) of your related comparison pages you usually arrange them by percentage solved. Eg,
https://www.12000.org/my_notes/CAS_integration_tests/reports/summer_2021/inch1.htm#x2-30001.2
Yet in this new page the results are given as:
Mathematica 13.0.1 95.636%
Maple 2022 95.848%
Maple also does soundly better on all your other metrics: Mean time (sec), mean leaf size, total time (min), and total leaf size.
And the name "Maple" comes before "Mathematica" alphabetically.
On Monday, April 18, 2022 at 6:22:32 AM UTC-4, Nasser M. Abbasi wrote:
FYI,
The following is a new report showing results of running
a large collection of ODE's using Maple and Mathematica
and comparing their performance
https://www.12000.org/my_notes/CAS_ode_tests/index.htm
Why does you table have Mathemetica placed in the row above that in
which Maple is placed?
In several (almost all?) of your related comparison pages you usually
arrange them by percentage solved. Eg,
https://www.12000.org/my_notes/CAS_integration_tests/reports/summer_2021/inch1.htm#x2-30001.2
Yet in this new page the results are given as:
Mathematica 13.0.1 95.636%
Maple 2022 95.848%
Maple also does soundly better on all your other metrics: Mean time
(sec), mean leaf size, total time (min), and total leaf size.
And the name "Maple" comes before "Mathematica" alphabetically.
acer schrieb:
On Monday, April 18, 2022 at 6:22:32 AM UTC-4, Nasser M. Abbasi wrote:
FYI,
The following is a new report showing results of running
a large collection of ODE's using Maple and Mathematica
and comparing their performance
https://www.12000.org/my_notes/CAS_ode_tests/index.htm
Why does you table have Mathemetica placed in the row above that in
which Maple is placed?
In several (almost all?) of your related comparison pages you usually arrange them by percentage solved. Eg,
https://www.12000.org/my_notes/CAS_integration_tests/reports/summer_2021/inch1.htm#x2-30001.2
Yet in this new page the results are given as:
Mathematica 13.0.1 95.636%
Maple 2022 95.848%
Maple also does soundly better on all your other metrics: Mean time
(sec), mean leaf size, total time (min), and total leaf size.
And the name "Maple" comes before "Mathematica" alphabetically.
Mathematica has been catching up rapidly over the last five years or
so. Will Maple really be able to stay ahead? This is mostly a question
of manpower only, I think.
FYI,
The following is a new report showing results of running
a large collection of ODE's using Maple and Mathematica
and comparing their performance
https://www.12000.org/my_notes/CAS_ode_tests/index.htm
The above page will now supersede the Kamke and Murphy
web pages I have as this new page includes them and many
additional ode's.
The Kamke and Murphy pages will no longer be updated
but will remain online.
I've collected these ode's over a long time and manually
entered them into sqlite3 database. These differential
equations were collected from many standard textbooks and
other sources such as Kamke and Murphy collections.
The current database included [8,836] odes as of today.
The following table summarizes the result
Percentage solved:
=====================
Mathematica 13.0.1 95.566 %
Maple 2022 95.817 %
Other stats are on the above page. I will add additional stats
as I continue updating the above page as the datebase grow.
The textbooks used are listed above (about 45 books as of now).
These are the same books and database I use for the following
web page which also has picture and more information
of the books used
http://localhost/my_notes/solving_ODE/index.htm
The above result shows that Mathematica and Maple are now
in a virtual tie in their ability to solve ode's and above
the rest of other CAS systems out there in this area.
No verification was done to check that the solutions are correct or not.
Also no grading on the solution is done, and no
post processing such as simplification.
All the commands used are listed for each ode.
Any problems/issues found, please let me know.
--Nasser
May I suggest you test ODE with mathHand.com? It can solve many ODE that other cannot. e.g. DrHuang.com/index/bug
May I suggest you test ODE with mathHand.com? It can solve many ODE that other cannot. e.g. DrHuang.com/index/bugAs far as I can tell, your bug list are all variations of the same bug that has, at some point, been fixed. Here are five examples from your list in Mathematica 13.1...
In[160]:= DSolve[y'[x] - y[x]^2 - 2 x^2 - 1 == 0, y[x], x]
Out[160]= {{y[
x] -> -(((1 + I) 2^(1/4) C[
1] (((1 +
I) x ParabolicCylinderD[-(1/4)
I (-2 I + Sqrt[2]), (1 + I) 2^(1/4) x])/2^(3/4) -
ParabolicCylinderD[
1 - 1/4 I (-2 I + Sqrt[2]), (1 + I) 2^(1/4) x]) - (1 -
I) 2^(1/4) (-(((1 - I) x ParabolicCylinderD[
1/4 I (2 I + Sqrt[2]), (-1 + I) 2^(1/4) x])/2^(3/4)) -
ParabolicCylinderD[
1 + 1/4 I (2 I + Sqrt[2]), (-1 + I) 2^(1/4) x]))/(C[
1] ParabolicCylinderD[-(1/4) I (-2 I + Sqrt[2]), (1 + I) 2^(
1/4) x] +
ParabolicCylinderD[
1/4 I (2 I + Sqrt[2]), (-1 + I) 2^(1/4) x]))}}
In[161]:= DSolve[y'[x] - 2 y[x]^2 - 2 x^2 - 1 == 0, y[x], x]
Out[161]= {{y[
x] -> -((2 (-1)^(1/4) C[
1] ((-1)^(1/4)
x ParabolicCylinderD[-(1/2) - I/2, 2 (-1)^(1/4) x] -
ParabolicCylinderD[1/2 - I/2, 2 (-1)^(1/4) x]) +
2 (-1)^(3/
4) ((-1)^(3/4)
x ParabolicCylinderD[-(1/2) + I/2, 2 (-1)^(3/4) x] -
ParabolicCylinderD[1/2 + I/2, 2 (-1)^(3/4) x]))/(2 (C[
1] ParabolicCylinderD[-(1/2) - I/2, 2 (-1)^(1/4) x] + ParabolicCylinderD[-(1/2) + I/2, 2 (-1)^(3/4) x])))}}
In[163]:= DSolve[y'[x] - 3 y[x]^2 - 2 x^2 - 1 == 0, y[x], x]
Out[163]= {{y[
x] -> -(((1 + I) 6^(1/4) C[
1] (((1 + I) 3^(1/4)
x ParabolicCylinderD[-(1/4)
I (-2 I + Sqrt[6]), (1 + I) 6^(1/4) x])/2^(3/4) -
ParabolicCylinderD[
1 - 1/4 I (-2 I + Sqrt[6]), (1 + I) 6^(1/4) x]) - (1 -
I) 6^(1/4) (-(((1 - I) 3^(1/4)
x ParabolicCylinderD[
1/4 I (2 I + Sqrt[6]), (-1 + I) 6^(1/4) x])/2^(3/4)) -
ParabolicCylinderD[
1 + 1/4 I (2 I + Sqrt[6]), (-1 + I) 6^(1/4) x]))/(3 (C[
1] ParabolicCylinderD[-(1/4)
I (-2 I + Sqrt[6]), (1 + I) 6^(1/4) x] +
ParabolicCylinderD[
1/4 I (2 I + Sqrt[6]), (-1 + I) 6^(1/4) x])))}}
In[165]:= DSolve[y''[x] - y'[x] y[x] - x == 0, y[x], x]
Out[165]= {{y[
x] -> -((2 ((-1)^(
3/4) (1/2 (-1)^(3/4)
x ParabolicCylinderD[-(1/2) I (-I + C[1]), (-1)^(3/4)
x] - ParabolicCylinderD[
1 - 1/2 I (-I + C[1]), (-1)^(3/4) x]) + (-1)^(1/4) C[
2] (1/2 (-1)^(1/4)
x ParabolicCylinderD[1/2 I (I + C[1]), (-1)^(1/4) x] -
ParabolicCylinderD[
1 + 1/2 I (I + C[1]), (-1)^(1/4)
x])))/(ParabolicCylinderD[-(1/2) I (-I + C[1]), (-1)^(
3/4) x] +
C[2] ParabolicCylinderD[1/2 I (I + C[1]), (-1)^(1/4) x]))}}
In[168]:=
DSolve[y'[x]^2 - x y'[x] - y[x] == 0, y[x], x] // FullSimplify
Out[168]= {{y[
x] -> (-4 E^(3 C[1])
x - (-2 x^2 + (-E^(6 C[1]) - 20 E^(3 C[1]) x^3 + 8 x^6 + Sqrt[
E^(3 C[1]) (E^(3 C[1]) - 8 x^3)^3])^(1/3))^2)/(
8 (-E^(6 C[1]) - 20 E^(3 C[1]) x^3 + 8 x^6 + Sqrt[
E^(3 C[1]) (E^(3 C[1]) - 8 x^3)^3])^(1/3))}, {y[x] ->
1/16 (8 x^2 + ((4 + 4 I Sqrt[3]) x (E^(3 C[1]) + x^3))/(-E^(
6 C[1]) - 20 E^(3 C[1]) x^3 + 8 x^6 + Sqrt[
E^(3 C[1]) (E^(3 C[1]) - 8 x^3)^3])^(
1/3) + (1 - I Sqrt[3]) (-E^(6 C[1]) - 20 E^(3 C[1]) x^3 +
8 x^6 + Sqrt[E^(3 C[1]) (E^(3 C[1]) - 8 x^3)^3])^(1/3))}, {y[
x] -> 1/16 (8 x^2 + ((4 - 4 I Sqrt[3]) x (E^(3 C[1]) + x^3))/(-E^(
6 C[1]) - 20 E^(3 C[1]) x^3 + 8 x^6 + Sqrt[
E^(3 C[1]) (E^(3 C[1]) - 8 x^3)^3])^(
1/3) + (1 + I Sqrt[3]) (-E^(6 C[1]) - 20 E^(3 C[1]) x^3 +
8 x^6 + Sqrt[E^(3 C[1]) (E^(3 C[1]) - 8 x^3)^3])^(1/3))}, {y[
x] -> (4 E^(3 C[1])
x - (-2 x^2 + (-E^(6 C[1]) + 20 E^(3 C[1]) x^3 + 8 x^6 + Sqrt[
E^(3 C[1]) (E^(3 C[1]) + 8 x^3)^3])^(1/3))^2)/(
8 (-E^(6 C[1]) + 20 E^(3 C[1]) x^3 + 8 x^6 + Sqrt[
E^(3 C[1]) (E^(3 C[1]) + 8 x^3)^3])^(1/3))}, {y[
x] -> ((-4 - 4 I Sqrt[3]) E^(3 C[1]) x + (4 + 4 I Sqrt[3]) x^4 +
8 x^2 (-E^(6 C[1]) + 20 E^(3 C[1]) x^3 + 8 x^6 + Sqrt[
E^(3 C[1]) (E^(3 C[1]) + 8 x^3)^3])^(
1/3) + (1 - I Sqrt[3]) (-E^(6 C[1]) + 20 E^(3 C[1]) x^3 +
8 x^6 + Sqrt[E^(3 C[1]) (E^(3 C[1]) + 8 x^3)^3])^(
2/3))/(16 (-E^(6 C[1]) + 20 E^(3 C[1]) x^3 + 8 x^6 + Sqrt[
E^(3 C[1]) (E^(3 C[1]) + 8 x^3)^3])^(1/3))}, {y[
x] -> (4 I (I + Sqrt[3]) E^(3 C[1]) x + (4 - 4 I Sqrt[3]) x^4 +
8 x^2 (-E^(6 C[1]) + 20 E^(3 C[1]) x^3 + 8 x^6 + Sqrt[
E^(3 C[1]) (E^(3 C[1]) + 8 x^3)^3])^(
1/3) + (1 + I Sqrt[3]) (-E^(6 C[1]) + 20 E^(3 C[1]) x^3 +
8 x^6 + Sqrt[E^(3 C[1]) (E^(3 C[1]) + 8 x^3)^3])^(
2/3))/(16 (-E^(6 C[1]) + 20 E^(3 C[1]) x^3 + 8 x^6 + Sqrt[
E^(3 C[1]) (E^(3 C[1]) + 8 x^3)^3])^(1/3))}}
The current result is
======================
System %solved Number solved Number failed
Maple 2022.1 94.454 9487 557
Mathematica 13.1 93.260 9367 677
FYI,
The following is a new report showing results of running
a large collection of ODE's using Maple and Mathematica
and comparing their performance
https://www.12000.org/my_notes/CAS_ode_tests/index.htm
The above page will now supersede the Kamke and Murphy
web pages I have as this new page includes them and many
additional ode's.
The Kamke and Murphy pages will no longer be updated
but will remain online.
I've collected these ode's over a long time and manually
entered them into sqlite3 database. These differential
equations were collected from many standard textbooks and
other sources such as Kamke and Murphy collections.
The current database included [8,836] odes as of today.
The following table summarizes the result
Percentage solved:
=====================
Mathematica 13.0.1 95.566 %
Maple 2022 95.817 %
On Monday, 18 April 2022 at 20:22:32 UTC+10, Nasser M. Abbasi wrote:
FYI,
The following is a new report showing results of running
a large collection of ODE's using Maple and Mathematica
and comparing their performance
https://www.12000.org/my_notes/CAS_ode_tests/index.htm
The above page will now supersede the Kamke and Murphy
web pages I have as this new page includes them and many
additional ode's.
The Kamke and Murphy pages will no longer be updated
but will remain online.
I've collected these ode's over a long time and manually
entered them into sqlite3 database. These differential
equations were collected from many standard textbooks and
other sources such as Kamke and Murphy collections.
The current database included [8,836] odes as of today.
The following table summarizes the result
Percentage solved:
=====================
Mathematica 13.0.1 95.566 %
Maple 2022 95.817 %
Other stats are on the above page. I will add additional stats
as I continue updating the above page as the datebase grow.
The textbooks used are listed above (about 45 books as of now).
These are the same books and database I use for the following
web page which also has picture and more information
of the books used
http://localhost/my_notes/solving_ODE/index.htm
The above result shows that Mathematica and Maple are now
in a virtual tie in their ability to solve ode's and above
the rest of other CAS systems out there in this area.
No verification was done to check that the solutions are correct or not.
Also no grading on the solution is done, and no
post processing such as simplification.
All the commands used are listed for each ode.
Any problems/issues found, please let me know.
--NasserMay I suggest you test ODE with mathHand.com? It can solve many ODE that other cannot. e.g. http://DrHuang.com/index/bug
FYI,
The following is a new report showing results of running
a large collection of ODE's using Maple and Mathematica
and comparing their performance
https://www.12000.org/my_notes/CAS_ode_tests/index.htm
| Sysop: | Keyop |
|---|---|
| Location: | Huddersfield, West Yorkshire, UK |
| Users: | 293 |
| Nodes: | 16 (2 / 14) |
| Uptime: | 224:16:09 |
| Calls: | 6,623 |
| Calls today: | 5 |
| Files: | 12,171 |
| Messages: | 5,318,481 |