  This paper continues to study linear and unconditionally modified-energy
stable (abbreviated as SAV-GL) schemes for the gradient flows. The schemes are
built on the SAV technique and the general linear time discretizations (GLTD)
as well as the extrapolation for the nonlinear term. Different from [44], the
GLTDs with three parameters discussed here are not necessarily algebraically
stable. Some algebraic identities are derived by using the method of
undetermined coefficients and further used to establish the modified-energy
inequalities for the unconditional modified-energy stability of the
semi-discrete-in-time SAV-GL schemes. It is worth emphasizing that those
algebraic identities or energy inequalities are not necessarily unique for some
choices of three parameters in the GLTDs. Numerical experiments on the
Allen-Cahn, the Cahn-Hilliard and the phase field crystal models with the
periodic boundary conditions are conducted to validate the unconditional
modified-energy stability of the SAV-GL schemes, where the Fourier
pseudo-spectral method is employed in space with the zero-padding to eliminate
the aliasing error and the time stepsizes for ensuring the original-energy
decay are estimated by using the stability regions of our SAV-GL schemes for
the test equation. The resulting time stepsize constraints for the SAV-GL
schemes are almost consistent with the numerical results on the above gradient
flow models.
