Solution of difficult steady state separation problems by use of the functional transformation method

An extension of the range of convergence of the classical Newton-Raphson method and modified forms of it by use of the functional transformation method is demonstrated herein by use of numerical examples of difficult- to-solve distillation problems. Variations of the Newton-Raphson method considered are as follows: (1) the 2N Newton-Raphson method with the Broyden modification; (2) the 2N Newton-Raphson method with the Broyden-Bennett modification; (3) the almost-band algorithm with the Broyden-Householder modification; (4) the almost-band algorithm with Schubert's modification; and (5) parametric continuation with step size selection by Gear's method.