APPLICATION OF MODIFIED NEWTON-RAPHSON METHODS IN MULTICOMPONENT EQUILIBRIUM PROBLEMS

A comprehensive study of the Newton-Raphson method and some of its mod ifications has been carried out on a set of complex, non-linear algebr aic equations arising out of the thermodynamic equilibria existing in the As-S-O vapor system. The modifications included are constant Jacob ian technique, second order correction to the original method, and the use of relaxation parameters. Several new parameters were incorporate d during the course of the study to facilitate convergence properties. The combination of parameters, yielding high confidence of convergenc e and low computation time were determined. The results obtained in th is study led to several semi-empirical guidelines for the numerical so lution of an arbitrary set of non-linear equations encountered in simi lar problems.