Dear Guilherme and rest of the developers,
I am not an specialist in DAE at all, but I just wanted to point out
that the function desolve_odeint on version >=4.6 already supports
stiff systems (via the BDF method). If you look at the documentation
of desolve_odeint you will find the example
#Another Stiff system with some optional parameters with no default
value:
sage: y1,y2,y3=var('y1,y2,y3')
sage: f1=77.27*(y2+y1*(1-8.375*1e-6*y1-y2))
sage: f2=1/77.27*(y3-(1+y1)*y2)
sage: f3=0.16*(y1-y3)
sage: f=[f1,f2,f3]
sage: ci=[0.2,0.4,0.7]
sage: t=srange(0,10,0.01)
sage: v=[y1,y2,y3]
sage:
sol=desolve_odeint(f,ci,t,v,rtol=1e-3,atol=1e-4,h0=0.1,hmax=1,hmin=1e-4,mxstep=1000,mxords=17)
which does compute the solution of a stiff system with a BDF method
(look at the scale of numbers with a line3d(sol)). It is pretty fast
and simple, since you only call the symbolic expression. The code
inside used cython so it is very quick.
As you point out, Scipy (on which desolve_odeint is based) does
already include some Dopri5 so maybe you could modifiy the
desolve_odeint function if necessary.
Hope it can help,
Joaquim Puig
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