Modelling of kinetic mechanisms

Many books are available with detailed and clear accounts of numerical integration and data handling. The first of these topics can be explained relatively succinctly to a level which should help the reader to understand the procedures for numerical solutions of differential equations describing 

Kinetic mechanisms are generally described by differential equations of the type 

In the simplest case with linear concentration terms (see section 2.4), as in A B, the differential equation 

The analytical solution in equation (2.2.2) can, of course, be graphically represented in terms of against t. The matrix method described in section 2.4 and other procedures applied to examples in sections 4.2 and 5.1, can be used to obtain solutions for rate equations describing quite complex reactions, as long as they are linear in concentration terms. For equations with non-linear terms it is usually not possible to obtain analytical solutions. In such cases the mechanism can only be described by a set of n — 1 differential equations for n reactants and one equation for conservation of mass. These have to be solved numerically. 

The solution of a set of coupled differential equations (DEs) describing a reaction is an initial value problem, which means that all c,s are known at some starting value Cj t=0). The basic principle of numerical solutions of DEs can be illustrated using Euler s stepping method on the three state 

---