Implementing unequal intervals explicit methods

It appears that most of the (published) use of unequal intervals is with the explicit method - specifically, the box method. There is no (overt) transformation function but rather some formula for the width of a given box i. Thus Feldberg s function, Eq. 5.69, is actually a restatement of 

Feldberg s (1981) use of the exponentially expanding space grid method, which states 

This brings in several problems. The first (and possibly least) is the fact that, since X must not exceed 0.5 anywhere and X is the highest, we have an exponentially decreasing X with i (distance from the electrode). The more serious problem is that in the discretisation, the usual small doubts enter imagine three adjacent boxes with width and 

This removes all the above problems and will be as accurate as Feldberg s (1981) corrected method, again with the X restriction as mentioned above. My feeling here is that, having gone to the trouble of using unequal intervals in order to reduce computing time, it makes sense to combine this with the Crank-Nicolson scheme to get the most out of it. 

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