The Numerical Integration of Kinetic Equations for Chemical Systems Having Both Slow and Fast Reactions.
An algorithm for finding conservation equations for a chemical system that includes widely variant reaction rates. When some reactions are much faster than others, the time step that can be traversed in one iteration of a numerical integration is essentially determined by the fastest reaction. Thus, for many steps, nothing important occurs in the slow reactions. To overcome this, fast reactions can be approximated by instantaneous reactions, whose equilibrium constants do not enter the integration routine except by way of the initial values of the substances. Any amount greater than zero will prevent undue rounding-off errors in floating-point computation. In this example, conservation equations of fast reactions are found by a JOSS program for the orthogonal complement of a matrix. Together with a RAND program (DAUX) that calculates the derivatives, a SHARE program is used to integrate the differential equations. The DAUX and JOSS routines are listed. 69 pp. Refs.