This report gives the result of running a number of partial diﬀerential equations in Mathematica and Maple. This is work in progress as more PDE’s are being added.
The following are the systems used
The following are plain text ﬁles of the current collection of the PDE’s used in this report.
10 minutes real time is used as the time limit to complete a problem. If CAS does not ﬁnish within this time limit, a failed score is given.
The PC used to run these tests is windows 10 professional 64 bit with 64 GB RAM running Intel core i7-8086K at 4 GHZ.
All possible options, assumptions and HINTS are tried to obtain a solution. The command
DSolve
is used in Mathematica and the command pdsolve
in Maple.
In this version, all results are automatically simpliﬁed. This is done to reduce the size of the ﬁnal solution.
It is possible I missed some option, assumption or HINT, which could help make the CAS able to solve a given PDE now marked as unsolved. Will correct such a case if found.
Most of the solutions returned are not veriﬁed. If a CAS returns a solution, it is assumed to be correct and that the problem was solved by the CAS.
These problems were collected from textbooks such as
PDE’s from other text books will be added with time.
Some problems were also collected from Maple and Mathematica help pages, documentation and technical forums.
Some of these problems I solved by hand. I have tried to verify that all hand solutions are
correct by verifying them using Maple’s pdetest()
. Will add more hand solutions in the
future in order to compare with the computer solution.
The following are some PDF ﬁles used to collect some problems from