[Maxima-discuss] Partial Differential Equations in Maxima

[José A. V. R. <jos...@gm...>]

Dear all:
As far as we know, there is no package in Maxima devoted to the solution of
partial differential equations or, more generally, the Fourier development
of piecewise-defined functions (yes, there is the package 'fourie', which
is very, very limited).
We have written one such package, called 'pdefourier'. It is available at
GitHub:
https://github.com/emmanuelroque/pdefourier
It comes with full documentation and lots of examples. Among other things,
the package can:
* Compute the Fourier coefficients or arbitrary piecewise-functions
(indeed, there is a companion package called 'piecewise' for dealing with
that kind of functions).
* Compute the whole Fourier series of piecewise-defined functions in
symbolic form, over arbitrary intervals
* Compute the truncated Fourier series, for graphical representations
* Solve the general regular Sturm-Liouville for the second-order linear
parabolic equation with constant coefficients (including the heat equation,
advection-difussion equation, and the like) in one dimension
* Solve the general regular Sturm-Liouville problem for the wave equation
in one and two dimensions (in the latter case, on rectabgular and circular
domains)
* Solve the Laplace and Poisson equations (the Laplace equation on
rectangles, disks, wedges and annuli, the Poisson equation on rectangles
and disks)
The GitHub page contains a few examples displayed, but in the documentation
folder there is a wxm file with many more.
An interesting feature is that the package is able of solving a lot of
equations on which Mathematica (versions 12.0 and 12.1) fails, and some for
which Maple fails too! Also, there are special commands for computing the
zeros of Bessel functions of the first kind and their derivatives.
We would like to hear your comments, suggestions, criticisms, etc.
All the best,

Emmanuel Roque
José Antonio Vallejo

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José Antonio Vallejo
Faculty of Sciences
State University of San Luis Potosi (Mexico)
http://galia.fc.uaslp.mx/~jvallejo
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