van der Pol equation about dassl.jl

[pwl]

I was deducing minimal allowed stepsize from eps(T) where T is the type of the time variable. When eps is changed to eps(t), where t is the current time your example works fine (the epsilon for t=0.0 is ~e-324...).

EDIT: After thinking about it, the van der Pol equation should be time independent, so starting from t=1.0 brings the bug back...

[mauro3]

How does the time step evolve? Your fix above suggests that the time step is >eps(1) at t1 even though the solution repeats after t1.6. Maybe it's a problem with the initial steps? Anyway, using eps(t) instead of eps(T) is probably good irrespective.

[pwl]

This fixes the two errors I made when implementing DASSL.

1. I was not using the initial value for the derivative properly (the dy0 keyword argument).
2. When dy0 was not given I was not obtaining it from solving F(t,y0,dy0)=0 for dy0.

These two errors combined were forcing the stepsize to go way below the sensible values thus causing the premature termination of integration due to h<hmin.

In this fix I also rewrote the way error estimates are generated and handled (now it's clearer and simpler) and I slightly changed the order/timestep selection strategy.

Now it is possible to run the solver (with or without Jacobian) with the local error tolerances reduced to 1e-14 and still have h>1e-16 (although for this particular example it leads to larger global error due to roundoff errors).

[mauro3]

thanks