Hello David,
Yes, I have written an implementation of this algorithm and have looked at ode1_lie to
get ideas. I knew there were problems with ode1_lie so I've decided to write a new implementation
to see if I could figure what the problems were. One problem was that the integrating factor can not depend
on y in the implemented method, lie_exact was not general enough (see Ibragimov, CRC handbook..).
Another problem that I have right now is that I need to be able to represent implicit solutions in a nice way.
I am now able to get the solutions of the first three examples given in the paper. I will test the fourth example
when this issue is resolved and then see about the kamke testsuite.
Regards,
Nijso
> Date: Thu, 28 Jan 2010 08:26:50 +1100
> From: dbmaxima at gmail.com
> To: nijso at hotmail.com
> CC: maxima at math.utexas.edu
> Subject: Re: [Maxima] max time limit for solve
>
> nijso beishuizen wrote:
> > Hi,
> >
> > The equation I try to solve is the final step in the solution of a
> > nonlinear ode. The solution in the paper
> > (of Cheb-Terrab and Kolokolnikov, it's on ArXiv) is given in implicit
> > form as:
> >
> > sol : x + 1/(3*x^3*(y+x)^3)+x^(1+a)/(1+a) = %c;
> >
> Nijso,
>
> Is this from E. S. Cheb-Terrab, T. Koloknikov, First Order ODEs,
> Symmetries and Linear Transformations, European Journal of Applied
> Mathematics, Vol. 14, No. 2, pp. 231-246 (2003)? I wrote an
> implementation of this as part of the contrib_ode function. Look in
> the share/contrib/diffequations/ directory. The code is ode1_lie.mac
> and the examples and unit tests are in the tests subdirectory
>
> The code works well for some cases but runs "forever" for other cases.
> There are a number of test cases from Kamke and Murphy that are
> commented out for this reason. I understand that the Maple routine
> doesn't have the same problem. I haven't been able to fix this.
>
> David
>
_________________________________________________________________
New Windows 7: Find the right PC for you. Learn more.
http://windows.microsoft.com/shop