We develop a robust algorithm for isothermal flash calculations of multi-component mixtures. The algorithm provides an explicit, parametric solution for a recent variation of the Rachford-Rice equation by employing a powerful analytical technique, namely the Adomian decomposition method. The computational speed of the algorithm is shown to be further enhanced by applying the iterated Shanks transformation. Unlike previous methods, our algorithm obviates the troublesome need for an initial guess, guarantees an excellent rate of convergence and is demonstrated to be more computationally economic than prior art. Several reliable examples from the literature, including the flash calculation for a mixture with nineteen components, as well as an extensive set of hypothetical, randomly-generated problems are presented to illustrate the exceptional efficacy of our new approach. (C) 2015 Elsevier B.V. All rights reserved.