Your opinion on a class of ODE problems

[Namir]

(01-22-2016 07:41 PM)ttw Wrote:  If you are not using a canned method, you might try deriving a method using 3 steps so that A is updated on steps 1(mod 3), B on steps 2(mod 3), and C on steps 0(mod 3). This type of overlapping update has helped in dynamic equations. Of course, (as I didn't derive anything), the error terms would have to be worked out.

I am using Runge-Kutta 4th order, Runge-Kutta Fehlberg, Cash-Karp, and Dormand–Prince ODE methods. I divide each interval into 10 sub-intervals. I then apply the ODE methods on the sub-intervals. At the end of each iteration of a sub-interval I re-calculate the concentration of one of the chemical, say compound A, as equal to the initial sum of concentrations (for all chemicals) minus the sum of the current concentrations of the other chemicals. This approach maintains the conservation of matter law.

I will do some more testing using reactions with known analytical solutions vs using the ODE methods. This kind of comparison will be very telling.

Namir