Your opinion on a class of ODE problems

[ttw]

I haven't looked at concentration equations but there are some formulations that try to conserve energy throughout long computations. You might look up some papers on these methods. Often they try to use midpoint differences or backward differences rather than forward differences. Perhaps some of the methods used to conserve energy could help in conserving mass.

I don't have access to journals (except for free ones on the net) so I can't check things out easily.

https://en.wikipedia.org/wiki/Leapfrog_integration

https://web.njit.edu/~jiang/math614/dahlquist.pdf

https://en.wikipedia.org/wiki/Numerical_..._equations

http://www.unige.ch/~hairer/preprints/santander.pdf

https://people.maths.ox.ac.uk/suli/nsodes.pdf

http://user.it.uu.se/~perl/ODE_07/NumODEsbook.pdf

These may give you some indication of what method to use.