  In this paper, we propose several novel numerical techniques to deal with
nonlinear terms in gradient flows. These step-by-step solving schemes, termed
3S-SAV and 3S-IEQ schemes, are based on recently popular scalar auxiliary
variable (SAV) and invariant energy quadratization (IEQ) approaches. In these
constructed numerical methods, the phase function $\phi$ and auxiliary variable
can be calculated step-by-step. Compared with the traditional SAV/IEQ
approaches, there are many advantages for the novel 3S-SAV/3S-IEQ schemes.
Firstly, we do not need the restriction of the bounded from below of the
nonlinear free energy potential/density function. Secondly, the auxiliary
variable combined with nonlinear function can be treated totally explicitly in
the 3S-SAV/3S-IEQ approaches. Specially, for solving the discrete scheme based
on IEQ approach, the linear system usually involves variable coefficients which
change at each time step. However, the discrete scheme based on 3S-IEQ approach
leads to linear equation with constant coefficients. Two comparative studies of
traditional SAV/IEQ and 3S-SAV/3S-IEQ approaches are considered to show the
accuracy and efficiency. Finally, we present various 2D numerical simulations
to demonstrate the stability and accuracy.
