Quasi steady state and partial equilibrium approximations: Their relation and their validity

The quasi steady state and partial equilibrium approximations are analysed in the context of a system of nonlinear differential equations exhibiting multiscale behaviour. Considering systems in the most general and dimensional form, it is shown that both approximations are limiting cases of leading-order asymptotics. Algorithmic conditions are established which guarantee that the accuracy and stability delivered by the two approximations are equivalent to those obtained with leading-order asymptotics. It is shown that the quasi steady state approximation is a limiting case of the partial equilibrium approximation. Algorithms are reported for the identification of the variables in quasi steady state and/or of the processes in partial equilibrium.