What happens to errors

This section is taken from a numerical text (Acton 1970). Digital evaluation always means a finite number of digits and each result will carry a small error. Let us add a small positive error e to all concentrations c and see what happens to it if we now evaluate the next c. Its actual value should be 

Independently of X, the error is propagated undiminished. However, an equal error on all c s is unlikely - more likely it will be of roughly equal magnitude on all c s but of fluctuating sign. Assume, as a simple model of this, that c and c carry +e and c carries -e error. Then 

Clearly, if X the error will grow in magnitude. There are more rigorous proofs and all point to an upper limit of H for X. As will be seen in Chapt. 6, the actual choice of X has a bearing on accuracy, as well as on the time taken for a simulation. In Chapt. 5 we present simulation schemes stable for all values of X. 

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