1.1 Introduction

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

1. Mathematica 12.2 (64 bit).
2. Maple 2021 (64 bit) with Physics version 959.

The following are plain text files of the current collection of the PDE’s used in this report.

Mathematica_PDE_IN_CAS_problems.txt

Maple_PDE_IN_CAS_problems.txt

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

1. Richard Haberman applied partial differential equations, 5th edition
2. David J Logan applied Partial differential equations.
3. Partial differential equations and boundary value problems with Maple by George A. Articolo, 2nd ed.
4. Handbook of first order partial differential equations (HFOPDE), Volume 1, by Polyanin, Zaitsev, Moussiaux (2002).
5. Handbook of nonlinear partial differential equations (HNPDE), by Polyanin, Zaitsev (2004).
6. Nonlinear Partial Differential Equations by Lokenath Debnath, 3rd edition. (2012).
7. Introduction to Partial Differential Equations by Peter J. Olver, Springer. (2014).

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

1. PDE_and_BC_during_december_2018.pdf
2. What_is_New_after_Maple_2018.pdf
3. Integral_Transforms_revamped_Oct_2019.pdf