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

This work has developed a simple, robust, and fast method for the solution of Underwood's equation f(x) for minimum reflux. The new scheme involves devising an iterative solver g by re-arranging this equation, obtaining a secondary function equal to g − x, and finally applying Ostrowski's fourth-order technique to find the roots of this function. The use of Ostrowski's method in place of Newton's popular second-order formula requires little extra calculation per iteration other than a function value at an auxiliary point. The novel method is successful where the direct applications of Newton's and Ostrowski's solvers to Underwood's equation fail. It keeps iterations within bounds and rapidly converges to the root of interest.