Two-Point Derivative Cases

For those who prefer to keep the derivative approximation of G down to the two-point form, the above can perhaps be simplified a little the u-v device is not needed as such, as only the first substitution (6.6) is required. 

It is arguable whether this is in fact simpler than the form for general n, (6.38), but it does avoid calling a function. 

the irreversible case is accommodated by setting Kb to zero. 

The reversible case gives rise to the same equation as for higher n as in (6.44) and thus to the system 

Up to this point, the treatments have involved reactions for which the discrete form of the reaction-diffusion equations involves only terms in concentration of the species to which the discrete equation applies. That is, if there were two substances involved, O and R as above, then the discrete equation at a point i had terms only in C q for species O, and only C r for species R. This made it straightforward to use the Thomas algorithm to reduce a system like (6.27) to (6.28), treating the two species systems separately. They then get coupled through the boundary conditions. 

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