General Solution of a System of Linear First-Order Rate Equations.

摘要

A simple method of solving a system of N linear first-order rate equations is given. The method gives the complete time-dependent solutions to the equations in terms of the system rate constants and initial conditions. The solutions are of the form of the sum of N exponentials whose characteristic times are the eigenvalues of the matrix constructed from the system rate constants. The coefficients of the exponentials are determined by the eignevectors of the rate constant matrix and the initial conditions. The method is especially suited to solution on a digital computer and requires only matrix manipulation and diagonalization subroutines. (Author)