Laasonen method improvements

The Laasonen method, because of the forward difference in T, has errors of 0(6T, H2), and the first-order behaviour with respect to ST limits its accuracy to about the same as the explicit method described in Chap. 5. However, it has a smooth error response to disturbances such as an initial transient (Cottrell), and is stable for any value of 6T/H2, where // is either the same as all intervals if equal intervals are used in X, or is the smallest (usually the first) intervai if unequal intervals are used. This makes the method interesting, and it will be seen below that it can be improved. For simplicity, the symbol A will be used below, and denotes the largest value of that parameter, that is, the value from the smallest interval in space in a given system. 

If a given her is of higher than first order, nonlinear terms arise in the dynamic equation(s). With terms, for example, in squared concentrations (see below), there is the danger, due to computational errors, that a concentration becomes negative, after which it can never be corrected. The technique CN is especially prone to this, because of the oscillations it engenders as a response to sharp transients such as a potential jump. This is one reason some workers prefer the Laasonen method or its improved offshoots, which have a smooth error response without any oscillations. With a Pearson start, however, CN can be used safely, without the appearance of negative concentrations. 

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