Remark on convergences

In all the above examples, Figs. 6.2 to 6.7, the convergence plots tend 

0(6T) or 0(H ). The reader might expect from the discussion in Sects. 

First of all, these 0(6T ) errors refer to a single 6T step, whereas in the simulation in the T-range 0 T 1 we take 6T steps. Generally, this reduces the error order by one. Tests show that it is in fact the discretisation of the second derivative which limits the accuracy, hence the 0(H ) error for all methods. We might say that, in view of this, we are lucky that the better methods (CN, RKI) give better results, since they suffer from the same error source. 

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