Steady state of stiff linear kinetic systems by a Markov matrix method

Abstract

The absence of detailed balance in systems containing pseudo-first-order reactions can cause the evaluation of steady-state concentrations to be a difficult computational problem. if the rate constants differ by many orders of magnitude, direct solution for these concentrations from the matrix of rate constants is not practical. The embedded Markov chain generated by the state-changes of one molecule has a transition matrix whose better separation of eigenvalues makes it more suitable for analysis than the matrix of rate constants. Solution for an eigenvector of this matrix by the method of inverse iteration provides an efficient means for obtaining steady-state concentrations.