An understanding of the chemistry of the interstellar medium necessarily transits by a modeling process, in which an attempt is made to account for the dominant reaction mechanisms. Such models incorporate a library of reactions and associated rate coefficients. The rates of many important reactions have been measured in the laboratory, although not always at the low temperatures at which they are required.
Theory can be a useful guide to the temperature dependence of a reaction rate.
A set of linear algebraic equations results, which may be solved by the Newton-Raphson method. The alternative technique involves solving the time-dependent equations, starting from appropriate initial conditions. This problem is non-trivial, because the first order differential equations which incorporate the rates of the chemical equations are characterized by widely differing time constants. In practice, the two methods yield the same results, to within numerical precision. It was generally believed that the steady state solution was independent on the initial conditions.