  In this paper, we carry out stability and error analyses for two first-order,
semi-discrete time stepping schemes, which are based on the newly developed
Invariant Energy Quadratization approach, for solving the well-known
Cahn-Hilliard and Allen-Cahn equations with general nonlinear bulk potentials.
Some reasonable sufficient conditions about boundedness and continuity of the
nonlinear functional are given in order to obtain optimal error estimates.
These conditions are naturally satisfied by two commonly used nonlinear
potentials including the double-well potential and regularized logarithmic
Flory-Huggins potential. The well-posedness, unconditional energy stabilities
and optimal error estimates of the numerical schemes are proved rigorously.
