In order to solve for corrections to initial estimate of composition
, Lagrangian multiplier
, moles n, and temperature T,
we will use a descent Newton-Raphson method. This method involves a Taylor
series expansion of the equation and use the terms of the first
order. The correction variables are
for the gases,
for the condensed species,
,
the dimensionless Lagrangian multipliers and
.
![]() |
(13) |
![]() |
(15) |
![]() |
(16) |