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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 developedInvariant Energy Quadratization approach, for solving the well-knownCahn-Hilliard and Allen-Cahn equations with general nonlinear bulk potentials.Some reasonable sufficient conditions about boundedness and continuity of thenonlinear functional are given in order to obtain optimal error estimates.These conditions are naturally satisfied by two commonly used nonlinearpotentials including the double-well potential and regularized logarithmicFlory-Huggins potential. The well-posedness, unconditional energy stabilitiesand optimal error estimates of the numerical schemes are proved rigorously.

Numerical approximations of the Cahn-Hilliard and Allen-Cahn Equations  with general nonlinear potential using the Invariant Energy Quadratization  approach