Your opinion on a class of ODE problems

[Namir]

(01-22-2016 05:45 AM)ttw Wrote:  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.

Thanks for the equations. You mentioned conservation of energy. My problem is similar to solving a system of ODEs that calculate temperatures of various connected objects, where the calculation "errors" end up violating the laws of conservation of energy.

I am using the system of ODE to calculate concentrations of chemicals used in optimization problems. So far, I have used chemical reactions whose ODE have analytical solutions. So I was fine. I am trying to stretch in dealing with chemical reactions whose ODE have no easy or published analytical solutions.