Ordinary differential equations in Maxima

> From:  Edmond Orignac
> 
> Hello all,
> 
> I am using maxima 5.9.3, built on CMUCL on Linux (Debian). 
> 
> I have noticed a few oddities in the packages for differential
> equations in Maxima. 
> 
> First, the ode2 package in maxima is able to solve the differential 
> equations for the Bessel functions. However, it is expressing the 
> solution (for integer n) using k1*%j[n](x)+k2*%y[n](x), whereas the
> bessel package is using bessel_j(n,x) and bessel_y(n,x) to represent
> these functions. This can probably be easily corrected by putting 
> the names for these functions in ode2.mac. 

Agree.  At present it needs to be fixed in src/ode2.lisp, which is a 
translation of ode2.mac.  I'll work up a patch.  

> Second, whereas the ode2 package can solve the differential equation
> for the Bessel functions, it cannot solve the ones defining 
> the modified
> Bessel functions or the Struve functions. Maybe it is possible to add
> this capability to ode2.mac by slightly extending the solver to deal
> with these particular cases.    

Barton Willis (http://www.unk.edu/facstaff/profiles/willisb/ has written
Maxima code for solving second order linear differential equations. 
It uses a method of Bronstein and Lafaille.  
http://www-sop.inria.fr/cafe/Manuel.Bronstein/publications/issac2002.pdf
I have plans to add it to share/contrib/diffequations.  The code works
in my local tree but the connection is a little rough.  I should just
commit it and polish it later.

> Third, I have noticed the existence of a differential equations
> package, in the share/diffequations 
> directory comprising the files pmain.mac, phygm.mac, odeaux.mac,
> pdvtr.mac, pivtr.mac. This package does not seem to be documented. 
> odeaux seems to be loading various packages to solve differential
> equations. 
> However, if loaded in maxima it is causing an error message caused
> by the line: 
> FOR I IN ODE_ROUTINELIST DO APPLY('setup_AUTOLOAD,I)),
>  sstatus(feature,"ode")))$
> 
> maxima complains that "\n FOR I is not an infix operator". 
> the package pmain is trying to solve the differential equation
> by loading an appropriate pachage. 
> The package phypgm is 
> solving the hypergeometric differential equation and the Legendre 
> equation. 
> For instance after loading phypgm, typing: 
>  x*(1-x)*'diff(y,x,2)+(c-(a+b+1))*'diff(y,x)-a*b*y=0;
> 
>  lode2(%o5);
> 
> gives a solution in terms of Riemann's P-function (though
> I am unsure about the correctness of the coefficients). 
> 
> Does anyone have some experiene with these differential equation 
> packages ?

I couldn't get any of the additional code in share/diffequations to 
work, but haven't built up the courage to archive it either.
I have added some stuff in share/contrib/diffequations for
first order ODEs.

	David


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