Selected asymptotic integration

The second approach is a fractional-step method we call asymptotic timestep-splitting. It is developed by consideration of the specific physics of the problem being solved. Stiffness in the governing equations can be handled "asymptotically" as well as implicitly. The individual terms, including those which lead to the stiff behavior, are solved as independently and accurately as possible. Examples of such methods include the Selected Asymptotic Integration Method (4,5) for kinetics problems and the asymptotic slow flow algorithm for hydrodynamic problems where the sound speed is so fast that the pressure is essentially constant (6, 2). ... 

The Selected Asymptotic Integration Method (5) has been utilized for many years at NRL for the solution of the coupled "stiff" ordinary differential equations associated with reactive flow problems. This program has been optimized for the ASC. 

As the concentration of the substance to be determined falls as a result of dissolution or depositing on the electrode, the electrolytic current also approaches zero asymptotically if the electrolytic process is conducted with a potential less than the half-wave potential of the substance in question. The electric charge consumed is measured with a coulometer or determined by integrating Equation (1). The advantage of this process is in the selectivity of the electrode processes, e.g. a determining process can be conducted for two metals with similar depositing behaviour. 

We have calculated theoretical curves from equation (12) in three steps (1) For a < 50 nc/kg equation (13) applies (2) for selected values of a in the range 50 < a < 1000 we carry out the integration in equation (12) numerically, using time intervals At = 80 days (3) for a > 1000 it is found that the asymptotic form of equation (12) is valid ... 

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