Two numerical algorithms having a quadratic convergence rate, the S-system and Newton's method, have been applied to a vapor phase epitaxy InGaAsP model, which is usually given by a stiff non-linear simultaneous equation, and their convergence performances have been examined in terms of the convergence radius and iteration numbers under various conditions, In the computations by the S-system method, over 99.9% calculations successfully converge from a roughly estimated initial setting for equilibrium partial pressures, where Newton's method completely cannot. The iteration numbers of the S-system method arc 10 or less times in most computations. This indicates that convergence process by the S-system method was carried out in a quadratic convergence rate like that of Newton's method. These results clearly show that the S-system method is always significantly superior to Newton's method. We conclude that the S-system method is the best method to solve the epitaxial thermodynamic model equations with a quadratic convergence rate. (C) 2002 Elsevier Science B.V. All rights reserved.