+ From:	ERICH::OOLI         14-OCT-1986 17:02  To:	KOST,OOLI          Subj:	ODE solvers   
 Hi Corrie,  :    Here are the results of my timing of three ODE solvers.  G I used a system of two equations. Both are relatively simple, involving H only linear and quadratic expressions. All calculations were carried out; in single precision. The error criterion was set to 10**-3.   ; RKC is the clear winner IF one chooses the stepsize wisely! H I obtained the best results when setting the stepsize H to onehalf timesE the integration intervall on the first call, then using the value RKC @ returns after this first call as input for all subsequent calls.  I Setting H to onehalf integration intervall before each call increases CPU  time by a factor of <= 2.   I Setting H to (intervall/64) as suggested in the UBC writeup increases CPU  time by a factor of about 5.  G Second fastest is DEABM from the SLATEC library, when the extrapolation F feature is allowed (see doc's). It appears to take about twice as longG as the optimum RKC runs. However, there appears to be an oscillation of J the solution about the "true" solution that is considerable and far beyond the error boundary!   N Third fastest is DERKF, also from SLATEC, roughly three times slower than RKC.  K Last one is DEABM with extrapolation disabled. In that case, DEABM is about ? four times slower than RKC, but the accuracy problems are gone.   K I should also mention that ONLY RKC ran all my cases without any complaint. M The SLATEC routines complained at different times about too small integration G intervalls, excessive demand on accuracy, even stiffness of the system.    The choice is therefore clear!   Uli     