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

[Roland S. <ma...@ro...>]

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_Loe
wy_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_ALL
TYPES_in_the_web/.

 

His implementation includes application to PDEs and to nonlinear
second-order ODEs. This CAS, publicly available at 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security certificate has run out of date recently.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