Re: [Maxima-discuss] Partial Differential Equations in Maxima

[Alfonso <alf...@gm...>]

This is really fantastic! Thank you very much!

Alfonso

On 02-04-20 12:50, José A. Vallejo Rodríguez wrote:
> 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
>
> _____________________________________
> José Antonio Vallejo
> Faculty of Sciences
> State University of San Luis Potosi (Mexico)
> http://galia.fc.uaslp.mx/~jvallejo
> _____________________________________
>
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