Why don't you read it up. That answer is practically useless.

What I read up contained some quite detailed maths which I mostly haven't come across. But from several internet searches it seems like actually quite a complicated field. Overall, my impression on a basic level is that we call the ODE system stiff if, of the different mathematically possible real solutions, a very wide range and/or difference exists (e.g. one solution is 10

^{9}, another 10

^{-9}) meaning that in predicting estimates for iteration we will find it very cumbersome to yield both answers which could be correct.

If I gave you one what will you do with it.

Mainly just wanted to see if the ODE itself looked any different from the ones we've already studied. Or if there is a visibly obvious reason from the ODE why it should be stiff. I guess I could just have asked. Sorry, if that would have been simpler for you.

Google's a good start.

I Googled "chemical kinetics equilibriated steps" and found nothing which seems to be of relevance. There was some stuff I found very interesting on a Wikipedia page that came up as a result (

http://en.wikipedia.org/wiki/Detailed_balance), which is vaguely to do with kinetics (it postulates that each reaction should actually be written as an equilibrium, i.e. reversible, and then throws up some details, interesting for me at least, about what is or is not possible if we treat reactions are irreversible), but I don't see what ostensibly is the approximation you mean by 'equilibriated steps'. On the Wikipedia page, the "approximation" is to make a series (cycle) of irreversible reactions into equilibria so that they are actually possible, but this is of course the opposite of an approximation, and in any case you've already shown me how to write the ODEs for equilibria as opposed to irreversible, the page doesn't go into approximations.

My question was a little open-ended before so I'll govern it now. Are there any more approximations I should be aware of, e.g. in the first few years of undergraduate study of kinetics? (Other than steady state) I bring this up because some of the stuff on the Wikipedia page I linked to is beyond me. If that is what you mean by equilibriated steps maybe it's better to ignore it for now.