An approximate analytical solution for the transient phase of the Michaelis-Menten reaction is derived using the Adomian decomposition method. The analytical solution, which is given in the form of a power series, is found to be highly accurate in predicting the behaviour of the reaction in the very early stages.
To accelerate the convergence of the power series solution and extend its region of applicability throughout the entire transient phase, we have used (a) the method of Padé approximants and (b) the iterated Shanks transformation. Both the Padé approximant and the Shanks transformation are shown to converge rapidly throughout and beyond the transient period and yield very accurate results. A comparison of the various analytical approximations and a direct numerical solution of the nonlinear initial value problem is also presented.