Simple, robust, and fast iterative solution of Underwood's equation for minimum reflux

Rapid and robust resolution of Underwood equations using convex transformations

“…This example (n = 7) is taken from Billingsley (2002) and was addressed previously by Leibovici and Nichita (2010), Kocak (2011) and . It corresponds to a sub-cooled feed (q = 2, « = −1).…”

“…(40) for bounds of the WA window, denoted L-WA, and of the WA␣ window, denoted L-WA␣). Several previous works (Leibovici and Neoschil, 1992;Michelsen and Mollerup, 2004;Kocak, 2011;Li et al, 2012) used the mid-interval as starting point and this option was added for comparison (related to intervals = ˛k +1 − ˛k and to the WA solution window). As opposed to the similar in nature Rachford-Rice equation, using the quasi-convex function and switching to the convex function if an iterate goes out of bounds (FGH) does not improve the convergence speed.…”

“…Leibovici and Nichita (2010) proposed two simple algorithms, one using a logistic function and the other removing both adjacent asymptotes. Kocak (2011) used a modified Ostrowski (1966) fourth-order method, and warned that such methods should be used with caution because iterates can fall out of the search interval. , Monroy-Loperena and and Vacahern and Monroy-Loperena (2012) presented an elegant solution by solving the problem as a generalized eigenvalue problem (finding all at once all the roots of Eq.…”