The Jacobian matrices given by both fixed-point algorithms are the same:
The full Newton algorithm leads to the following derivative matrix of the activity coefficients:
The following Jacobian matrix is also obtained:
For the scenario with a low ionic strength, the Jacobian matrices are equivalent for the full Newton and fixed-point algorithms, leading to similar Newton steps ().
The high ionic strength scenario starts with an initial component activities equal to 5.0 10-4 mol.L-1for all components. The ionic strength equals 1.197 mol.L-1. The species concentrations, activity values and first Newton steps proposed by the fixed-point algorithm (inner and outer) and full Newton algorithm are given in Table 3 .
Table 3: Initial values for the situation with a high ionic strength.