Implementing unequal intervals Crank-Nicolson

Let us again assume Feldberg s function, Eq. resulting Eq. 5.79 The discrete form of Eq the CN scheme, is then 

The second, forward pass, using the known value, is then identical with that for equal intervals, see Sect. 5.2, Eq. 5.43. Programming details can be seen in the program VARX in the final chapter. 

For unequal time intervals, we look at the example transformed diffusion equation 5.85. This is to be discretised at intervals of SO and H. We use index j to count 0 intervals and i to count X intervals (of H). 

To make proper use of the Crank-Nicolson philosophy, according to which the second-order expression (the right-hand side of Eq. 5.85) should be approximated by the mean of the discrete expressions at time T and the new time T+8T (here 0 and need to use the two different X 

This can again be rearranged into the familiar 3-band system of equations 

---