This describes the codes and results which allow the comparison of
MEBDF.f ,Radau5.f , sprint.f and lsode.f on various test problems.
The code mebdf.f is being updated to allow the solution of daes
and it is hoped to release this new code in the near future.


The tables of results for running various codes on the scaled
DETEST test set are given in the file detest.compare.  results given
are for    stride, radau5, lsode, desi and mebdf

All results were obtained by running in double precision on an IBM RS6000.

Also of possible interest is the mebdf code which is called mebdf.f.
This code is also in NETLIB and will soon be replaced by a code which
will also deal with DAEs.

To obtain the detest results for mebdf it is necessary to compile 

     MEBDF.f      det.f and tempdet.f

This is explained in DETEST.COMPARE

Results with rtol=atol are obtained by running MEBDF.f ,det.f and newdet.f.
with these results corresponding to  the option itol=5.

Results on the unscaled version of detest with itol=5 and rtol=atol are
obtained by running MEBDf.f , unscaled.f and unscnew.f.




Results for the 4 codes MEBDF, RADAU5, LSODE and SPRINT are given in
mebdffinal.res,   rad.res, lsode.res and sprint.res.  The drivers
are in mebdfhold.progs, rad.progs, lsode.progs and sprint.progs.
These are the results and drivers for the problems
vdp, robertson, hires, oreg, e5, beam, plate, cusp, bruss and KS
explained in Hairer and Wanner.
Results are also given for the well known B5 problem of DETEST
and for a more difficult version of the 'ring' problem.



Mebdf also has a sparse option to allow it to be used as the
time integrator in MOL.  Some results are given for the chemical
flooding problem.  (see also A.C. Hindmarsh, Lawrence Livermore Laboratory,
rep :avoiding BDF stability Barriers in the MOL solution of Advection
Dominated problems and Applied Numerical Mathematics, vol17, 1995,pp311.).
Results on this problem are given for the 4 codes sprint, lsode,radau5
and mebdf.   It is not claimed that this method of solution is in any
way optimal.  It is used simply to generate an IVP of dimension 50000
which should be large enough to test out if there are severe
storage limitations and if the banded matrix option is correct.



Finally, results are given for a heat equation with a non-zero rhs.
This problem is explained on page 75 equation (16) of
The MOL Solution of Time Dependent Partial Differential Equations,
Computers Math with Appl, vol 31, no 11, 69-78, 1996.  
The drivers run this problem with NTOP=1,5,10,20,50 .  As NTOP
increases the problem becomes more nonlinear and function/ Jacobian
evaluations become very expensive.  It therefore gives a profile of the
behavoiur of the various codes.

The author would be happy to receive any comments!



The code mebdf.f has been put in Netlib 
and appears as ode/dmebdf.f.


It is hoped that there will be some co-operation between Geneva,
London and Amsterdam to present test problems and results.  My
web will soon be changed to reflect this.Z