Modeling and numerical solutions of vapor phase epitaxy are limited because of convergence ability and a large number of iterations. To overcome these limitations, for the first time two Newton-like methods have been applied to models of vapor phase epitaxy for GaAs and InxGa1-xP: The Newton-Raphson method (NRM) and the power-law formalism method (PLFM). We compare the performances of the two methods In terms of the ability of convergence and the iteration numbers. The results indicate that PLFM is always significantly superior to NRM. All calculations by PLFM successfully converge from a rough estimated initial values for equilibrium partial pressures, where NRM can not. These results suggest that the Limitation in the numerical calculations of the vapor growth epitaxy can be widely extended by the application of PLFM.