Computational singular perturbation CSP theory

The CSP technique [126-130] has been developed by Lam and Goussis as a formal method for analyzing reaction mechanisms. It is specifically designed to enable the user to establish partial-equilibrium and quasisteady-state relationships without using any chemical intuition or expertise. The basis of the technique is to rewrite equations (4.1) and (4.2) in terms of a new set of basis vectors, rather than the physical representation using 

Stoichiometric and reaction rate vectors. By choosing this new basis set in an optimum way, information about the ordering of time-scales can be seen more easily. 

Again we consider the basic rate equation (4.1). As described in equation (4.2), the reaction rate column vector f is usually written in the form 

Let aj(t), i = 1,2. N, be a set of N linearly independent column basis vectors with inverse b (0- The reaction rate vector f can be rewritten as 

This new representation is mathematically identical to the equations (4.1) and (4.2) regardless of the choice of the matrix of new basis vectors Af. 

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