Nonlinear Differential Equations: Application to Chemical Kinetics

Abstract

The laws governing chemical kinetics can be written as systems of ordinary differential equations. In the case of complex reactions with several different participating molecules, these equations are nonlinear and present interesting mathematical properties (stability, periodicity, bifurcation, etc.). The numerical solution of this type of system is a domain of study in itself with a flourishing literature. Very efficient numerical methods to solve systems of ODEs are implemented in MATLAB, as in most such software. The first model of reaction that we shall study in this chapter can be completely solved using such a standard package. We will therefore use the ode solvers provided by MATLAB , assuming that the user masters the underlying theory and the basic concepts such as convergence, stability, and precision (see Chap. 1).