Jacobian matrix equilibrium calculations

C.M. Bethke (52) has shown that significant numerical advantages in such calculations can be realized by switching into the basis set a mineral species that is in partial equilibrium with the aqueous phase. This avoids expansion of the size of the Jacobian matrix and reduces computation time. A method based on this concept is being developed for use in the 3270 version of EQ3/6. The concept appears to show promise for improvement of the "optimizer" algorithm as well as the Newton-Raphson one. 

To study the stability of the steady-sliding equilibrium point, the eigenvalues of the Jacobian matrix (evaluated at y = 0) are calculated. The Jacobian matrix is given by (F 0, O 0)... 

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