Reduction Methods for Chemical Systems

Abstract

Many systems studied in chemical kinetics can be posed as a high order nonlinear differential system with slow and fast variables. This has given an impetus to the development of methods that reduce the order of the differential systems but retain a desired degree of accuracy. This research has led to a rapidly expanding volume of papers devoted to reduction methods. All these methods are connected with the integral manifold method in one way or another. These connections were clearly given by H. Kaper and T. Kaper in (Physica D 165:66–93, 2002), which also gives a good overview of reduction methods in chemical kinetics. In this chapter we will use results given previously in parallel with our interpretation of the connection between the two most often used reduction methods and demonstrate that both methods may be replaced successfully by regular procedures of approximation of slow integral manifolds which were described in Chap. 5.