In this work an explicit expression for Jacoby matrix of m-phase n-component phase equilibrium equations set is proposed. In the case of 2-phase n-component equilibrium this matrix nonsingularity, on condition that the phase diagram singularities are absent, is proved. Explicit expression of this matrix opens up possibilities for developing general classification of phase diagram singularities and allows significantly accelerate phase equilibrium calculation procedure, especially in case of high n and m.
Also, in this work a linear differential equations set for the phase boundaries partial derivatives with respect to external parameters (alloy gross-composition, temperature, pressure, magnetic/electric field strength) is proposed. We called it the generalized Van der Waals equations set. It is shown, that matrix of this equations set can be reduced to the form, which is fully equivalent to Jacoby matrix of the corresponding phase equilibrium equations set. On the assumption of calculated phase equilibrium this equations set allows to precalculate in the first approximation the next equilibrium, which corresponds to the new value of external parameter. Realization of such a phase boundaries precalculation allows to essentially accelerate the whole phase diagram calculation procedure.