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Stable schemes with lower dispersion and diffusion errors are proposed.
Entropy stable schemes can be constructed with a specific choice of the numerical flux function.
A new family of stiffly stable schemes is employed in mixed explicit/implicit time-intgration rules.
Unconditionally energy stable schemes are used to solve the PFC model.
In the case of Navier Stokes equations, entropy variables are used to construct stable schemes.
We now recall the notion of fixed point iteration schemes and virtually stable schemes defined in [5].
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An energy stable scheme is developed for the three-phase flow system.
To our knowledge, this is the first such energy stable scheme for the PFC amplitude equations.
The allocation of the stress, velocity and electric field components on a staggered grid leads to a stable scheme.
By some subtle explicit implicit treatments, we obtain a linear coupled energy stable scheme for systems with dynamic contact line conditions and a linear decoupled energy stable scheme for systems with static contact line conditions.
We show that a stable scheme can be obtained by introducing a predictor step for the wave terms.
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