[Help-gsl] Performance issue with ODE solvers

[Sebastien Maret]

Hello,

I need to solve a large system (~500 equations) of stiff kinetic
chemical ODEs. I have tried to solve this system using both Gear M=1
implicit solver from the GSL, as well as the CVODE solver, which is
now part of the SUNDIALS library (1).

Although they both give the same solution, the program that use the
GSL is about ten times slower than the one that use the CVODE library,
for the same accuracy.

Looking at the time step (h) used by both solver, it seems that the
GSL one is consistently smaller (up to factor 100), which may explain
why the program that use the GSL runs much slower. I have made a plot
of the time step h vs. time t for both solvers (2).

I am rather confused by these differences. The fact that both programs
give the same results make me think that it's not a bug in my program,
but a real performance difference between the two solvers. Maybe the
GSL solvers are not suited to solve such a large systems of stiff
equations? I have tried to use other implicit solvers from the GSL
(except for bsimp, which require the Jacobian), and they all have
similar performance.

My program is rather big, so I am not posting it here. I could try to
see if I can reproduce the problem with a simpler program, if this is
useful.

Sebastien

(1) http://www.llnl.gov/CASC/sundials/
(2) http://www.astro.lsa.umich.edu/~smaret/download/step.pdf