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Application of Modified Newton-Raphson Methods in Multi-Component Equilibrium Problems

A comprehensive study of the Newton-Raphson method and some of its modifications has been carried out on a set of complex, non-linear algebraic equations arising out of the thermodynamic equilibria existing in the As-S-O vapor system. The modifications included are constant Jacobian technique, second order correction to the original method, and the use of relaxation parameters. Several new parameters were incorporated during the course of the study to facilitate convergence properties. The combination of parameters, yielding high confidence of convergence and low computation time were determined. The results obtained in this study led to several semi-empirical guidelines for the numerical solution of an arbitrary set of non-linear equations encountered in similar problems