The real-life example again

a few details on the use of CN. Eqs. 7.31-7.33 contain the second-order terms They are discretised, at point i, using the linearising approximation Eq. 7.41, to 

This produces a messy trio of equation systems at point i for each 

Strictly, there is a sufficient number (3m) of equations for the 3m unknowns so the system of equations can be solved. In practice, one might well give up at this point - especially in view of the fact that, if derivative boundary conditions are involved (as in quasi reversible electron transfer, the rule rather than the exception), we would also need to bring in the implicit boundary value algorithm. 

For some simpler mechanisms, CN (or ICN) will not turn out quite so impractical and is found to be a very good method, with the advantage of an unrestricted X value. 

We now apply second-order whole-system RKI to the example mechanism, equations 7.31 - 7.33. We need three arrays, for the three species  

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