Re: [Maxima-discuss] Solving linear ODEs, linear PDEs, and nonlinear second-order ODEs by decompostion

[Dimiter P. <dim...@gm...>]

Hi Roland,

Seems very interesting.
I think the linear case is straightforward to implement.

best regards,

Dimiter

On Sat, Feb 27, 2021 at 12:21 AM Roland Salz <ma...@ro...> wrote:

> Hi,
>
>
>
> recently I found an article by Fritz Schwarz, a German mathematician
> working for a Fraunhofer Institute close to Bonn, which describes a method
> generalizing Loewy decomposition of linear ODEs, see
>
>
>
> https://en.wikipedia.org/wiki/Loewy_decomposition,
>
>
>
> or, in more detail,
>
>
>
>
> https://www.researchgate.net/profile/Fritz-Schwarz/publication/280622202_Loewy_decomposition_of_linear_differential_equations/
> .
>
>
>
> While the above mentioned paper describes the application of this method
> to linear PDEs, in the following one this method is generalized to
> nonlinear second-order ODEs
>
>
>
>
> https://www.researchgate.net/publication/321221979_Decomposition_of_ordinary_differential_equations/
> .
>
>
>
> The author has implemented this method himself in a CAS called ALLTYPES,
> which I had never heard of before, see
>
>
>
>
> https://www.researchgate.net/profile/Fritz-Schwarz/publication/234774923_ALLTYPES_in_the_web/
> .
>
>
>
> His implementation includes application to PDEs and to nonlinear
> second-order ODEs. This CAS, publicly available at *alltypes.de
> <http://alltypes.de>*, seems not to be maintained actually, because my
> browser warns me about loading it, the security certificate has run out of
> date recently. From what I read the site is maintained by Zuse Institute,
> Berlin (ZIB), so I wrote them a mail about that point. Don’t know whether
> it will get to the right person, though. I did not look into the site yet.
>
>
>
> Well, I just wanted to give this information to the Maxima team, just in
> case there happens to be someone who might be interested in implementing
> this method in Maxima. I think it could be a quantum leap in solving
> differential equations, just as Albert Rich’s *Rubi* would be for
> integration.
>
>
>
> Best regards,
>
> Roland
>
>
>
>
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